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VOLUME OF SQUARE AND RECTANGULAR PYRAMIDS, AND THE VOLUME OF CYLINDER. (MG)
Objectives: At the end of the lesson, the learners will be able to: 1. explain inductively the volume of a cylinder using the area of a circle, leading to the identification of the formula. a. correctly determines the dimension of a cylinder; b. correctly determines the relationship between the cylinder and the area of a circle; and c. correctly derives the formula for finding the volume of a cylinder. 2. find the volume of a cylinder. 3. solve problems involving the volumes of cylinders
Volume Calculation Practice Use the formula for the volume of a cylinder (where r is the radius and h is the height) to solve the following problems. 1.A water bottle has a radius of 3 cm and a height of 15 cm. ⚬ Volume: ________________________ 2.A candle has a diameter of 5 cm (radius = 2.5 cm) and a height of 10 cm. ⚬ Volume: ________________________
Real-World Scenarios 1.Buying a Can of Paint ⚬ Volume of the can: V=602.88 cubic inches ⚬ Relation to area: The volume helps determine how much paint is needed for the area. 2.Lunchbox Packing ⚬ Volume of the can: V=28.27 cubic inches ⚬ Other items to compare: Sandwiches, fruit, or other cylindrical items.
3. Construction Application ⚬ Volume of the pillar: V=31.42 cubic feet ⚬ Importance: Knowing the volume is crucial for calculating material needs.
SAMPLE PROBLEM 1.What is the volume of a cylinder with a radius of 6 inches and a height of 12 inches? Use π = 3.14. 2.A cylinder has a diameter of 14 cm and a height of 20 cm. Find its volume. Use π = 3.14. 3.The volume of a cylinder is 1000π cm³. If the height of the cylinder is 20 cm, what is its radius?
SOLUTION: Solutions: 1.Volume = πr²h = π(6²)(12) = π(36)(12) = 432π in³ = 1356.48 in³ Radius = diameter/2 = 14/2 = 7 cm
2. Volume = πr²h = π(7²)(20) = π(49)(20) = 980π cm³ = 3073.2 cm³
3. Volume = πr²h 1000π = πr²(20) 1000 = r²(20) r² = 50 r = 50 = 7.07 cm √
ACTIVITY: VOLUME CALCULATION STATIONS
Station 1: Calculate the volume of a cylinder with a radius of 3 cm and a height of 5 cm. • Formula: • V=πr²h • Calculations: ⚬ Radius (r): __________ cm ⚬ Height (h): __________ cm ⚬ Volume (V): __________ cm³
Station 2: Find the height of a cylinder with a volume of 150 cm³ and a radius of 2.5 cm. • Formula: • V=πr²h • Calculations: ⚬ Radius (r): __________ cm ⚬ Height (h): __________ cm ⚬ Volume (V): __________ cm³
Station 3: Determine the radius of a cylinder with a volume of 1000 cm³ and a height of 10 cm. • Formula: • V=πr²h • Calculations: ⚬ Radius (r): __________ cm ⚬ Height (h): __________ cm ⚬ Volume (V): __________ cm³
Divide students into small groups and have them rotate through each station, solving the problems collaboratively. Encourage them to discuss their thought processes and strategies as they work together. This hands-on approach promotes teamwork and reinforces their understanding of volume calculations.
Station 1: Calculate the Volume • Volume (V): Approximately 141.3 cm³ Station 2: Find the Height • Height (h): Approximately 4.8 cm Station 3: Determine the Radius • Radius (r): Approximately 5.64 cm
VOLUME PROBLEM-SOLVING JOURNAL WORKSHEET Name: _____________________________ Date: _____________________________
Instructions In this journal, you will record your understanding of deriving the volume formula for a cylinder, solve assigned volume problems, and reflect on your problem-solving process. Be sure to show your work and explain your reasoning for each problem.
Part 1: Understanding the Volume Formula Deriving the Volume Formula: Write down the formula for the volume of a cylinder and explain how you derived it. Volume Formula: V=πr²h Explanation:
Part 2: Volume Problems Problem 1: Calculate the volume of a cylinder with a radius of 4 cm and a height of 10 cm. Show your work: Volume (V): _______________ cm³
Problem 2: A cylinder has a volume of 500 cm³ and a radius of 5 cm. Find its height. Show your work: Height (h): _______________ cm
Problem 3: Determine the radius of a cylinder with a volume of 1000 cm³ and a height of 20 cm. Show your work: Radius (r): _______________ cm
Part 3: Reflection Challenges Faced Describe any challenges you encountered while solving these problems. Strategies Used What strategies did you use to overcome these challenges? Next Steps What will you do differently in future problem- solving activities?
Problem 3: Determine the radius of a cylinder with a volume of 1000 cm³ and a height of 20 cm. Show your work: Radius (r): _______________ cm
REFLECTION QUESTION • How does understanding the volume of a cylinder help you in real-life situations, such as in cooking, construction, or packaging?
VOLUME OF A CYLINDER MULTIPLE CHOICE TEST Name: _____________________________ Date: _____________________________
Instructions Select the best answer for each question. 1. What is the formula for the volume of a cylinder? A) A) V=πr³ B) V=πr²h C) V=2πrh D) V=1/3πr² h
2. If a cylinder has a radius of 3 cm and a height of 7 cm, what is its volume? (Use π 3.14) ≈ A) 66.12 cm³ B) 94.2 cm³ C) 21.78 cm³ D) 31.42 cm³
3. A cylinder has a volume of 200 cm³ and a radius of 5 cm. What is its height? A) 8 cm B) 10 cm C) 6.4 cm D) 5 cm
4. Which of the following statements about the volume of a cylinder is true? A) The volume increases as the height decreases. B) The volume is independent of the radius. C) The volume can be calculated using the area of the base multiplied by the height. D) The volume formula does not involve π.
5. If the height of a cylinder is doubled while keeping the radius constant, how does this affect the volume? A) The volume remains the same. B) The volume doubles. C) The volume triples. D) The volume decreases by half.
Answer Key (For Teacher Use) 1.B 2.A 3.A 4.C 5.B
DAY 2 SUB-TOPIC: CALCULATE VOLUME OF A CYLINDER
VOLUME OF SHAPES REVIEW GAME WORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions In this activity, you will match different 3D shapes with their corresponding volume formulas. Work in pairs or small groups to discuss your answers. Matching Activity Match each 3D shape with the correct volume formula by writing the letter of the formula next to the corresponding shape. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Reflection Questions 1.Which volume formula do you find the easiest to remember? Why? 2.How does understanding these formulas help you in solving volume problems? 3.Discuss with your group: Can you think of real- world examples where you might need to calculate the volume of these shapes? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Answer key: 1.B 2.A 3.C 4.D 5.E hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
REAL-WORLD APPLICATIONS DISCUSSION WORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions In this activity, you will discuss real-world applications of cylinders and the importance of understanding their volume. Work in pairs or small groups to answer the questions and share your thoughts with the class. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Scenario 1: Soda Can Volume You are buying a 12-ounce can of soda. The can is cylindrical with a height of 4.8 inches and a diameter of 2.13 inches. How can you calculate the volume of the can to determine how much liquid it can hold? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
1.Calculate the Volume ⚬ Radius (r): __________ inches ⚬ Height (h): __________ inches ⚬ Volume (V): __________ cubic inches 2.Reflection Why is it important to know the volume of a soda can? How can this information be useful in real life? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Scenario 2: Pipe Volume in Plumbing In plumbing, cylindrical pipes are used to transport water and other fluids. If a pipe has a radius of 2 inches and a length of 10 feet, how can you calculate its volume to determine its capacity hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
1.Calculate the Volume ⚬ Radius (r): __________ inches ⚬ Length (l): __________ feet ⚬ Volume (V): __________ cubic inches 2.Reflection • Why is it important to know the volume of a pipe in plumbing? How can this information be useful in real life? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Answer Key: Scenario 1: Soda Can Volume 1.Calculate the Volume ⚬ Radius (r): 1.065 inches ⚬ Height (h): 4.8 inches ⚬ Volume (V): Approximately 3.59 cubic inches hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
1.Reflection • Knowing the volume of a soda can is important for understanding how much liquid it can hold, which is useful for consumers and manufacturers in packaging and serving sizes. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Scenario 2: Pipe Volume in Plumbing 1.Calculate the Volume ⚬ Radius (r): 2 inches ⚬ Length (l): 120 inches (10 feet) ⚬ Volume (V): Approximately 25.13 cubic inches hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
2. Reflection • Knowing the volume of a pipe is crucial in plumbing to ensure it can transport the required amount of water or fluid efficiently, impacting system design and functionality. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
INTERACTIVE VOLUME CALCULATION DEMONSTRATION WORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions Follow along with the demonstration as we calculate the volume of a cylinder using the formula V=πr2h. Fill in the blanks and answer the questions as we go through each step. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Volume Formula Components 1.Volume (V): The amount of space inside the cylinder. ⚬ Definition: ______________________________________________ ________ 2.Radius (r): The distance from the center of the base to the edge. ⚬ Definition: _________________________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
3. Height (h): The distance from the base to the top of the cylinder. ⚬ Definition: _____________________________________ _________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Example Calculation Given: • Radius (r): 4 cm • Height (h): 10 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Step 1: Write down the formula V=πr²h Step 2: Substitute the values into the formula V=π(4² ) (10) Calculate r2 : 42 = 16 Substitute r² back into the formula: V=π (16 ) (10) hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Step 3: Multiply by height (h) Calculate r² * h: 16 * 10=__________ (Answer: 160) Substitute back into the formula: V= π (160) hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Step 4: Final Calculation Use 3.14 to find the volume: ≈ V=160 * 3.14=__________ (Answer: 502.4 cm³) ≈ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Reflection Questions 1.What did you learn about each component of the volume formula? 2.Why is it important to understand how to calculate volume? 3.Can you think of a real-world application where you would need to calculate the volume of a cylinder? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Sample Problem 1 Given: • Radius (r): 5 cm • Height (h): 12 cm 1.Write down the formula: V=πr2h Substitute values into the formula: V=π(52) * 12 hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
2. Calculate: ⚬ r2=__________ • Volume: ⚬ V=__________ • Final Volume: ⚬ ≈ __________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Sample Problem 2 Given: • Radius (r): 3 cm • Height (h): 8 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
1.Write down the formula: V=πr²h 2. Substitute values into the formula: V=π(3²)* 8 hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
3. Calculate: ⚬ r²=__________ • Volume: ⚬ V=__________ • Final Volume: ⚬ ≈__________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Sample Problem 3 Given: • Radius (r): 6 cm • Height (h): 15 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
1.Write down the formula: V=πr²h 2. Substitute values into the formula: V=π(62)* 15 hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
3. Calculate: ⚬ r2=__________ • Volume: ⚬ V=__________ • Final Volume: ⚬ ≈__________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
VOLUME CALCULATION RELAY WORKSHEET Name of Team: _____________________________ Team Members: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions In this relay race, your team will solve volume problems involving cylinders at different stations. Each team member will run to a station, solve the problem, and then tag the next teammate. Make sure to show your work for each problem! hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Formula: V=πr²h • Calculations: ⚬ Volume (V): __________ cm³ ⚬ Height (h): __________ cm ⚬ Radius (r): __________ cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Station 1: Calculate the Volume Problem: Calculate the volume of a cylinder with a radius of 5 cm and a height of 12 cm. Station 2: Find the Height Problem: A cylinder has a volume of 200 cm³ and a radius of 3 cm. What is its height? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Station 3: Calculate the Volume Problem: Calculate the volume of a cylinder with a radius of 4 cm and a height of 10 cm. Station 4: Find the Radius Problem: A cylinder has a volume of 500 cm³ and a height of 10 cm. What is its radius? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
ANSWER KEY Station 1: Calculate the Volume • Volume (V): Approximately 942 cm³ Station 2: Find the Height • Height (h): Approximately 7.07 cm Station 3: Calculate the Volume • Volume (V): Approximately 502 cm³ Station 4: Find the Radius • Radius (r): Approximately 5 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
VOLUME CALCULATION EXIT TICKET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions Solve the following volume problems independently. Show your work and explain your reasoning for each problem. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 1 What is the volume of a cylinder with a radius of 6 cm and a height of 15 cm? Problem 2 A cylinder has a volume of 500 cm³ and a radius of 5 cm. What is its height? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 3 Determine the radius of a cylinder with a volume of 1000 cm³ and a height of 20 cm. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
ANSWER KEY: Problem 1 • Volume (V): Approximately 565.5 cm³ Problem 2 • Height (h): Approximately 6.37 cm Problem 3 • Radius (r): Approximately 7.07 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
REFLECTION What did you find most challenging about solving these volume problems? What strategies did you use to overcome any difficulties? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
DAY 3-4 SUB-TOPIC: SOLVE WORD PROBLEMS INVOLVING VOLUME OF CYLINDER hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
VOLUME JEOPARDY WORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions Participate in the Jeopardy-style game by answering questions related to volume concepts. Each category contains questions of varying difficulty. Write your answers in the space provided. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
1.Categories 2.Volume Formulas 3.Real-Life Applications 4.Word Problems hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Category 1: Volume Formulas Question 1: What is the formula for the volume of a cylinder? Answer: ______________________________________________________ ______ Question 2: What does the variable "h" represent in the volume formula? Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Question 3: If the radius is doubled, how does that affect the volume? Answer: ______________________________________ ______________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Category 2: Real-Life Applications Question 1: How would you calculate the volume of a water tank that is cylindrical in shape? Answer: ______________________________________________________ ______ Question 2: Why is it important to know the volume of a pipe in plumbing? Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Question 3: Give an example of a product that uses cylindrical packaging and explain its volume significance. Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Category 3: Word Problems Question 1: A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? Answer: ______________________________________________________ ______ Question 2: If a cylindrical can holds 500 cm³ of soup, what is its height if the radius is 5 cm? Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Question 3: A cylindrical barrel has a volume of 1000 cm³ and a height of 20 cm. What is its radius? Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
REAL-WORLD APPLICATION BRAINSTORM WORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions Participate in the brainstorming session by thinking about where you encounter cylinders in everyday life. Use the prompts below to guide your thoughts and write down your ideas. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Brainstorming Prompts 1.Water Bottles ⚬ How do you calculate the volume of a water bottle? 2.Cooking ⚬ Why is it important to know the volume of a cylindrical container when cooking? 3.Construction ⚬ Where do you see cylinders used in construction, and how does knowing their volume help? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
4. Manufacturing ⚬ What cylindrical products do you encounter in manufacturing, and why is volume important for these products? 5. Cylindrical Furniture ⚬ How do cylindrical shapes appear in furniture design (e.g., tables, stools), and why is volume relevant? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
6. Transportation ⚬ In what ways are cylinders used in transportation (e.g., tires, fuel tanks), and how does understanding their volume matter? 7. Sports Equipment ⚬ Identify any sports equipment that uses cylindrical shapes (e.g., basketballs, cans of tennis balls). How does volume play a role in their design? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
8. Medical Containers ⚬ Discuss the importance of knowing the volume of cylindrical medical containers (e.g., vials, syringes) in healthcare. 9. Art and Design ⚬ How do artists or designers use cylindrical shapes in their work (e.g., sculptures, vases)? Why is understanding volume important for them? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
10. Beverage Cans ⚬ Why is it important to calculate the volume of beverage cans when designing packaging? 11. Cylindrical Storage ⚬ How does knowing the volume of cylindrical storage containers (e.g., barrels, bins) affect inventory management hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
WORD PROBLEM WALK WORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions As you walk around the classroom, you will encounter different word problems involving the volume of cylinders. Work with your partner to read and solve each problem. Write down your answers and any calculations you perform in the space provided. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 1 A cylindrical can has a radius of 4 cm and a height of 10 cm. What is its volume? • Calculations: • Volume (V): __________ cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 2 A swimming pool is in the shape of a cylinder with a radius of 5 feet and a height of 3 feet. How much water can it hold? • Calculations: • Volume (V): __________ ft³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 3 A juice container is cylindrical with a radius of 6 inches and a height of 8 inches. What is the volume of the container? • Calculations: • Volume (V): __________ in³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 4 A cylindrical pipe has a radius of 2 inches and a length of 12 inches. What is its volume? • Calculations: • Volume (V): __________ in³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 5 A water tank is shaped like a cylinder with a radius of 4 meters and a height of 10 meters. How much water can it store? • Calculations: • Volume (V): __________ m³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 6 A candle is in the shape of a cylinder with a diameter of 3 cm and a height of 15 cm. What is its volume? • Calculations: • Volume (V): __________ cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 1 • Volume (V): Approximately 502.4 cm³ Problem 2 • Volume (V): Approximately 235.6 ft³ Problem 3 • Volume (V): Approximately 1,146.9 in³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 4 • Volume (V): Approximately 150.8 in³ Problem 5 • Volume (V): Approximately 502.4 m³ Problem 6 • Volume (V): Approximately 106.1 cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
GROUP PROBLEM-SOLVING CHALLENGE WORKSHEET Group Members: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Instructions Work together as a group to solve the following word problems involving the volume of cylinders. Discuss your strategies and ensure everyone understands the steps taken to find the solutions. After solving, be prepared to present one problem and your solution to the class. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 1 If a can of soup has a height of 12 cm and a radius of 4 cm, what is the volume? Problem 2 A cylindrical tank has a radius of 3 meters and a height of 5 meters. How much water can it hold? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 3 A juice bottle is cylindrical with a radius of 5 cm and a height of 15 cm. What is its volume? Problem 4 A cylindrical water tank has a diameter of 4 feet and a height of 10 feet. How much water can it store? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 5 A candle has a height of 8 cm and a radius of 3 cm. What is its volume? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
ANSWER KEY: Problem 1 • Volume (V): Approximately 603 cm³ Problem 2 • Volume (V): Approximately 141.4 m³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 3 • Volume (V): Approximately 1,178.1 cm³ Problem 4 • Volume (V): Approximately 251.2 ft³ Problem 5 • Volume (V): Approximately 226.2 cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
VOLUME WORD PROBLEM EXIT TICKET Problem 1 A cylindrical container has a radius of 6 cm and a height of 8 cm. What is its volume? Problem 2 If a cylindrical water tank is 10 feet tall and has a radius of 4 feet, how much water can it hold? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Problem 3 A soup can has a height of 12 cm and a radius of 5 cm. What is the volume of the can? Problem 4 A cylindrical vase has a diameter of 10 cm and a height of 15 cm. What is its volume? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
Answers: Problem 1 • Volume: Approximately 452.4 cm³ Problem 2 • Volume: Approximately 502.7 ft³ Problem 3 • Volume: Approximately 314.2 cm³ Problem 4 • Volume: Approximately 1178.1 cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
REFLECTION QUESTION How did participating in the volume- related activities enhance your understanding of calculating the volume of cylinders and its real-world applications? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com ASSESSMENT
hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com Question 1 A cylindrical container has a radius of 3 cm and a height of 10 cm. What is its volume? A) 30π cm³ B) 90π cm³ C) 60π cm³ D) 15π cm³
hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com Question 2 If a cylindrical tank has a radius of 5 feet and a height of 8 feet, how much water can it hold? A) 100π ft³ B) 200π ft³ C) 250π ft³ D) 300π ft³
hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com Question 3 A candle has a diameter of 4 cm and a height of 10 cm. What is its volume? (Use π 3.14π 3.14) ≈ ≈ A) Approximately 50.24 cm³ B) Approximately 125.6 cm³ C) Approximately 31.4 cm³ D) Approximately 80 cm³
hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com ANSWER KEY: 1.B 2.B 3.B
REFERENCES • Mallari, K. G. (2024-2025). Lesson exemplar for mathematics grade 7: Quarter 2, Lesson 4 (Week 4). City College of San Fernando Pampanga • DepEd MATATAG Curriculum • Mallari, K. G. (2024-2025). Worksheet for mathematics grade 7: Quarter 2, Lesson 4 (Week 4). City College of San Fernando Pampanga hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
For more games, visit Hivessel.com Don't forget to support us in our socials below! hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com

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MATH-7-Quarter-2-Week-4-sxzdw2252525.pptx

  • 2.
    VOLUME OF SQUARE ANDRECTANGULAR PYRAMIDS, AND THE VOLUME OF CYLINDER. (MG)
  • 3.
    Objectives: At the endof the lesson, the learners will be able to: 1. explain inductively the volume of a cylinder using the area of a circle, leading to the identification of the formula. a. correctly determines the dimension of a cylinder; b. correctly determines the relationship between the cylinder and the area of a circle; and c. correctly derives the formula for finding the volume of a cylinder. 2. find the volume of a cylinder. 3. solve problems involving the volumes of cylinders
  • 4.
    Volume Calculation Practice Usethe formula for the volume of a cylinder (where r is the radius and h is the height) to solve the following problems. 1.A water bottle has a radius of 3 cm and a height of 15 cm. ⚬ Volume: ________________________ 2.A candle has a diameter of 5 cm (radius = 2.5 cm) and a height of 10 cm. ⚬ Volume: ________________________
  • 5.
    Real-World Scenarios 1.Buying aCan of Paint ⚬ Volume of the can: V=602.88 cubic inches ⚬ Relation to area: The volume helps determine how much paint is needed for the area. 2.Lunchbox Packing ⚬ Volume of the can: V=28.27 cubic inches ⚬ Other items to compare: Sandwiches, fruit, or other cylindrical items.
  • 6.
    3. Construction Application ⚬Volume of the pillar: V=31.42 cubic feet ⚬ Importance: Knowing the volume is crucial for calculating material needs.
  • 7.
    SAMPLE PROBLEM 1.What isthe volume of a cylinder with a radius of 6 inches and a height of 12 inches? Use π = 3.14. 2.A cylinder has a diameter of 14 cm and a height of 20 cm. Find its volume. Use π = 3.14. 3.The volume of a cylinder is 1000π cm³. If the height of the cylinder is 20 cm, what is its radius?
  • 8.
    SOLUTION: Solutions: 1.Volume = πr²h =π(6²)(12) = π(36)(12) = 432π in³ = 1356.48 in³ Radius = diameter/2 = 14/2 = 7 cm
  • 9.
    2. Volume =πr²h = π(7²)(20) = π(49)(20) = 980π cm³ = 3073.2 cm³
  • 10.
    3. Volume =πr²h 1000π = πr²(20) 1000 = r²(20) r² = 50 r = 50 = 7.07 cm √
  • 11.
  • 12.
    Station 1: Calculatethe volume of a cylinder with a radius of 3 cm and a height of 5 cm. • Formula: • V=πr²h • Calculations: ⚬ Radius (r): __________ cm ⚬ Height (h): __________ cm ⚬ Volume (V): __________ cm³
  • 13.
    Station 2: Findthe height of a cylinder with a volume of 150 cm³ and a radius of 2.5 cm. • Formula: • V=πr²h • Calculations: ⚬ Radius (r): __________ cm ⚬ Height (h): __________ cm ⚬ Volume (V): __________ cm³
  • 14.
    Station 3: Determinethe radius of a cylinder with a volume of 1000 cm³ and a height of 10 cm. • Formula: • V=πr²h • Calculations: ⚬ Radius (r): __________ cm ⚬ Height (h): __________ cm ⚬ Volume (V): __________ cm³
  • 15.
    Divide students intosmall groups and have them rotate through each station, solving the problems collaboratively. Encourage them to discuss their thought processes and strategies as they work together. This hands-on approach promotes teamwork and reinforces their understanding of volume calculations.
  • 16.
    Station 1: Calculatethe Volume • Volume (V): Approximately 141.3 cm³ Station 2: Find the Height • Height (h): Approximately 4.8 cm Station 3: Determine the Radius • Radius (r): Approximately 5.64 cm
  • 17.
    VOLUME PROBLEM-SOLVING JOURNAL WORKSHEET Name:_____________________________ Date: _____________________________
  • 18.
    Instructions In this journal,you will record your understanding of deriving the volume formula for a cylinder, solve assigned volume problems, and reflect on your problem-solving process. Be sure to show your work and explain your reasoning for each problem.
  • 19.
    Part 1: Understandingthe Volume Formula Deriving the Volume Formula: Write down the formula for the volume of a cylinder and explain how you derived it. Volume Formula: V=πr²h Explanation:
  • 20.
    Part 2: VolumeProblems Problem 1: Calculate the volume of a cylinder with a radius of 4 cm and a height of 10 cm. Show your work: Volume (V): _______________ cm³
  • 21.
    Problem 2: Acylinder has a volume of 500 cm³ and a radius of 5 cm. Find its height. Show your work: Height (h): _______________ cm
  • 22.
    Problem 3: Determinethe radius of a cylinder with a volume of 1000 cm³ and a height of 20 cm. Show your work: Radius (r): _______________ cm
  • 23.
    Part 3: Reflection ChallengesFaced Describe any challenges you encountered while solving these problems. Strategies Used What strategies did you use to overcome these challenges? Next Steps What will you do differently in future problem- solving activities?
  • 24.
    Problem 3: Determinethe radius of a cylinder with a volume of 1000 cm³ and a height of 20 cm. Show your work: Radius (r): _______________ cm
  • 25.
    REFLECTION QUESTION • Howdoes understanding the volume of a cylinder help you in real-life situations, such as in cooking, construction, or packaging?
  • 26.
    VOLUME OF ACYLINDER MULTIPLE CHOICE TEST Name: _____________________________ Date: _____________________________
  • 27.
    Instructions Select the bestanswer for each question. 1. What is the formula for the volume of a cylinder? A) A) V=πr³ B) V=πr²h C) V=2πrh D) V=1/3πr² h
  • 28.
    2. If acylinder has a radius of 3 cm and a height of 7 cm, what is its volume? (Use π 3.14) ≈ A) 66.12 cm³ B) 94.2 cm³ C) 21.78 cm³ D) 31.42 cm³
  • 29.
    3. A cylinderhas a volume of 200 cm³ and a radius of 5 cm. What is its height? A) 8 cm B) 10 cm C) 6.4 cm D) 5 cm
  • 30.
    4. Which ofthe following statements about the volume of a cylinder is true? A) The volume increases as the height decreases. B) The volume is independent of the radius. C) The volume can be calculated using the area of the base multiplied by the height. D) The volume formula does not involve π.
  • 31.
    5. If theheight of a cylinder is doubled while keeping the radius constant, how does this affect the volume? A) The volume remains the same. B) The volume doubles. C) The volume triples. D) The volume decreases by half.
  • 32.
    Answer Key (ForTeacher Use) 1.B 2.A 3.A 4.C 5.B
  • 33.
    DAY 2 SUB-TOPIC: CALCULATEVOLUME OF A CYLINDER
  • 34.
    VOLUME OF SHAPESREVIEW GAME WORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 35.
    Instructions In this activity,you will match different 3D shapes with their corresponding volume formulas. Work in pairs or small groups to discuss your answers. Matching Activity Match each 3D shape with the correct volume formula by writing the letter of the formula next to the corresponding shape. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 36.
  • 37.
    Reflection Questions 1.Which volumeformula do you find the easiest to remember? Why? 2.How does understanding these formulas help you in solving volume problems? 3.Discuss with your group: Can you think of real- world examples where you might need to calculate the volume of these shapes? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 38.
  • 39.
    REAL-WORLD APPLICATIONS DISCUSSION WORKSHEET Name:_____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 40.
    Instructions In this activity,you will discuss real-world applications of cylinders and the importance of understanding their volume. Work in pairs or small groups to answer the questions and share your thoughts with the class. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 41.
    Scenario 1: SodaCan Volume You are buying a 12-ounce can of soda. The can is cylindrical with a height of 4.8 inches and a diameter of 2.13 inches. How can you calculate the volume of the can to determine how much liquid it can hold? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 42.
    1.Calculate the Volume ⚬Radius (r): __________ inches ⚬ Height (h): __________ inches ⚬ Volume (V): __________ cubic inches 2.Reflection Why is it important to know the volume of a soda can? How can this information be useful in real life? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 43.
    Scenario 2: PipeVolume in Plumbing In plumbing, cylindrical pipes are used to transport water and other fluids. If a pipe has a radius of 2 inches and a length of 10 feet, how can you calculate its volume to determine its capacity hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 44.
    1.Calculate the Volume ⚬Radius (r): __________ inches ⚬ Length (l): __________ feet ⚬ Volume (V): __________ cubic inches 2.Reflection • Why is it important to know the volume of a pipe in plumbing? How can this information be useful in real life? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 45.
    Answer Key: Scenario 1:Soda Can Volume 1.Calculate the Volume ⚬ Radius (r): 1.065 inches ⚬ Height (h): 4.8 inches ⚬ Volume (V): Approximately 3.59 cubic inches hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 46.
    1.Reflection • Knowing thevolume of a soda can is important for understanding how much liquid it can hold, which is useful for consumers and manufacturers in packaging and serving sizes. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 47.
    Scenario 2: PipeVolume in Plumbing 1.Calculate the Volume ⚬ Radius (r): 2 inches ⚬ Length (l): 120 inches (10 feet) ⚬ Volume (V): Approximately 25.13 cubic inches hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 48.
    2. Reflection • Knowingthe volume of a pipe is crucial in plumbing to ensure it can transport the required amount of water or fluid efficiently, impacting system design and functionality. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 49.
    INTERACTIVE VOLUME CALCULATION DEMONSTRATIONWORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 50.
    Instructions Follow along withthe demonstration as we calculate the volume of a cylinder using the formula V=πr2h. Fill in the blanks and answer the questions as we go through each step. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 51.
    Volume Formula Components 1.Volume(V): The amount of space inside the cylinder. ⚬ Definition: ______________________________________________ ________ 2.Radius (r): The distance from the center of the base to the edge. ⚬ Definition: _________________________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 52.
    3. Height (h):The distance from the base to the top of the cylinder. ⚬ Definition: _____________________________________ _________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 53.
    Example Calculation Given: • Radius(r): 4 cm • Height (h): 10 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 54.
    Step 1: Writedown the formula V=πr²h Step 2: Substitute the values into the formula V=π(4² ) (10) Calculate r2 : 42 = 16 Substitute r² back into the formula: V=π (16 ) (10) hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 55.
    Step 3: Multiplyby height (h) Calculate r² * h: 16 * 10=__________ (Answer: 160) Substitute back into the formula: V= π (160) hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 56.
    Step 4: FinalCalculation Use 3.14 to find the volume: ≈ V=160 * 3.14=__________ (Answer: 502.4 cm³) ≈ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 57.
    Reflection Questions 1.What didyou learn about each component of the volume formula? 2.Why is it important to understand how to calculate volume? 3.Can you think of a real-world application where you would need to calculate the volume of a cylinder? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 58.
    Sample Problem 1 Given: •Radius (r): 5 cm • Height (h): 12 cm 1.Write down the formula: V=πr2h Substitute values into the formula: V=π(52) * 12 hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 59.
    2. Calculate: ⚬ r2=__________ •Volume: ⚬ V=__________ • Final Volume: ⚬ ≈ __________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 60.
    Sample Problem 2 Given: •Radius (r): 3 cm • Height (h): 8 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 61.
    1.Write down theformula: V=πr²h 2. Substitute values into the formula: V=π(3²)* 8 hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 62.
    3. Calculate: ⚬ r²=__________ •Volume: ⚬ V=__________ • Final Volume: ⚬ ≈__________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 63.
    Sample Problem 3 Given: •Radius (r): 6 cm • Height (h): 15 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 64.
    1.Write down theformula: V=πr²h 2. Substitute values into the formula: V=π(62)* 15 hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 65.
    3. Calculate: ⚬ r2=__________ •Volume: ⚬ V=__________ • Final Volume: ⚬ ≈__________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 66.
    VOLUME CALCULATION RELAY WORKSHEET Nameof Team: _____________________________ Team Members: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 67.
    Instructions In this relayrace, your team will solve volume problems involving cylinders at different stations. Each team member will run to a station, solve the problem, and then tag the next teammate. Make sure to show your work for each problem! hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 68.
    Formula: V=πr²h • Calculations: ⚬ Volume(V): __________ cm³ ⚬ Height (h): __________ cm ⚬ Radius (r): __________ cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 69.
    Station 1: Calculatethe Volume Problem: Calculate the volume of a cylinder with a radius of 5 cm and a height of 12 cm. Station 2: Find the Height Problem: A cylinder has a volume of 200 cm³ and a radius of 3 cm. What is its height? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 70.
    Station 3: Calculatethe Volume Problem: Calculate the volume of a cylinder with a radius of 4 cm and a height of 10 cm. Station 4: Find the Radius Problem: A cylinder has a volume of 500 cm³ and a height of 10 cm. What is its radius? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 71.
    ANSWER KEY Station 1:Calculate the Volume • Volume (V): Approximately 942 cm³ Station 2: Find the Height • Height (h): Approximately 7.07 cm Station 3: Calculate the Volume • Volume (V): Approximately 502 cm³ Station 4: Find the Radius • Radius (r): Approximately 5 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 72.
    VOLUME CALCULATION EXITTICKET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 73.
    Instructions Solve the followingvolume problems independently. Show your work and explain your reasoning for each problem. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 74.
    Problem 1 What isthe volume of a cylinder with a radius of 6 cm and a height of 15 cm? Problem 2 A cylinder has a volume of 500 cm³ and a radius of 5 cm. What is its height? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 75.
    Problem 3 Determine theradius of a cylinder with a volume of 1000 cm³ and a height of 20 cm. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 76.
    ANSWER KEY: Problem 1 •Volume (V): Approximately 565.5 cm³ Problem 2 • Height (h): Approximately 6.37 cm Problem 3 • Radius (r): Approximately 7.07 cm hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 77.
    REFLECTION What did youfind most challenging about solving these volume problems? What strategies did you use to overcome any difficulties? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 78.
    DAY 3-4 SUB-TOPIC: SOLVEWORD PROBLEMS INVOLVING VOLUME OF CYLINDER hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 79.
    VOLUME JEOPARDY WORKSHEET Name:_____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 80.
    Instructions Participate in theJeopardy-style game by answering questions related to volume concepts. Each category contains questions of varying difficulty. Write your answers in the space provided. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 81.
    1.Categories 2.Volume Formulas 3.Real-Life Applications 4.WordProblems hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 82.
    Category 1: VolumeFormulas Question 1: What is the formula for the volume of a cylinder? Answer: ______________________________________________________ ______ Question 2: What does the variable "h" represent in the volume formula? Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 83.
    Question 3: Ifthe radius is doubled, how does that affect the volume? Answer: ______________________________________ ______________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 84.
    Category 2: Real-LifeApplications Question 1: How would you calculate the volume of a water tank that is cylindrical in shape? Answer: ______________________________________________________ ______ Question 2: Why is it important to know the volume of a pipe in plumbing? Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 85.
    Question 3: Givean example of a product that uses cylindrical packaging and explain its volume significance. Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 86.
    Category 3: WordProblems Question 1: A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? Answer: ______________________________________________________ ______ Question 2: If a cylindrical can holds 500 cm³ of soup, what is its height if the radius is 5 cm? Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 87.
    Question 3: Acylindrical barrel has a volume of 1000 cm³ and a height of 20 cm. What is its radius? Answer: ______________________________________________________ ______ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 88.
    REAL-WORLD APPLICATION BRAINSTORM WORKSHEET Name:_____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 89.
    Instructions Participate in thebrainstorming session by thinking about where you encounter cylinders in everyday life. Use the prompts below to guide your thoughts and write down your ideas. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 90.
    Brainstorming Prompts 1.Water Bottles ⚬How do you calculate the volume of a water bottle? 2.Cooking ⚬ Why is it important to know the volume of a cylindrical container when cooking? 3.Construction ⚬ Where do you see cylinders used in construction, and how does knowing their volume help? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 91.
    4. Manufacturing ⚬ Whatcylindrical products do you encounter in manufacturing, and why is volume important for these products? 5. Cylindrical Furniture ⚬ How do cylindrical shapes appear in furniture design (e.g., tables, stools), and why is volume relevant? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 92.
    6. Transportation ⚬ Inwhat ways are cylinders used in transportation (e.g., tires, fuel tanks), and how does understanding their volume matter? 7. Sports Equipment ⚬ Identify any sports equipment that uses cylindrical shapes (e.g., basketballs, cans of tennis balls). How does volume play a role in their design? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 93.
    8. Medical Containers ⚬Discuss the importance of knowing the volume of cylindrical medical containers (e.g., vials, syringes) in healthcare. 9. Art and Design ⚬ How do artists or designers use cylindrical shapes in their work (e.g., sculptures, vases)? Why is understanding volume important for them? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 94.
    10. Beverage Cans ⚬Why is it important to calculate the volume of beverage cans when designing packaging? 11. Cylindrical Storage ⚬ How does knowing the volume of cylindrical storage containers (e.g., barrels, bins) affect inventory management hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 95.
    WORD PROBLEM WALKWORKSHEET Name: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 96.
    Instructions As you walkaround the classroom, you will encounter different word problems involving the volume of cylinders. Work with your partner to read and solve each problem. Write down your answers and any calculations you perform in the space provided. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 97.
    Problem 1 A cylindricalcan has a radius of 4 cm and a height of 10 cm. What is its volume? • Calculations: • Volume (V): __________ cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 98.
    Problem 2 A swimmingpool is in the shape of a cylinder with a radius of 5 feet and a height of 3 feet. How much water can it hold? • Calculations: • Volume (V): __________ ft³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 99.
    Problem 3 A juicecontainer is cylindrical with a radius of 6 inches and a height of 8 inches. What is the volume of the container? • Calculations: • Volume (V): __________ in³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 100.
    Problem 4 A cylindricalpipe has a radius of 2 inches and a length of 12 inches. What is its volume? • Calculations: • Volume (V): __________ in³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 101.
    Problem 5 A watertank is shaped like a cylinder with a radius of 4 meters and a height of 10 meters. How much water can it store? • Calculations: • Volume (V): __________ m³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 102.
    Problem 6 A candleis in the shape of a cylinder with a diameter of 3 cm and a height of 15 cm. What is its volume? • Calculations: • Volume (V): __________ cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 103.
    Problem 1 • Volume(V): Approximately 502.4 cm³ Problem 2 • Volume (V): Approximately 235.6 ft³ Problem 3 • Volume (V): Approximately 1,146.9 in³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 104.
    Problem 4 • Volume(V): Approximately 150.8 in³ Problem 5 • Volume (V): Approximately 502.4 m³ Problem 6 • Volume (V): Approximately 106.1 cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 105.
    GROUP PROBLEM-SOLVING CHALLENGE WORKSHEET GroupMembers: _____________________________ Date: _____________________________ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 106.
    Instructions Work together asa group to solve the following word problems involving the volume of cylinders. Discuss your strategies and ensure everyone understands the steps taken to find the solutions. After solving, be prepared to present one problem and your solution to the class. hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 107.
    Problem 1 If acan of soup has a height of 12 cm and a radius of 4 cm, what is the volume? Problem 2 A cylindrical tank has a radius of 3 meters and a height of 5 meters. How much water can it hold? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 108.
    Problem 3 A juicebottle is cylindrical with a radius of 5 cm and a height of 15 cm. What is its volume? Problem 4 A cylindrical water tank has a diameter of 4 feet and a height of 10 feet. How much water can it store? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 109.
    Problem 5 A candlehas a height of 8 cm and a radius of 3 cm. What is its volume? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 110.
    ANSWER KEY: Problem 1 •Volume (V): Approximately 603 cm³ Problem 2 • Volume (V): Approximately 141.4 m³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 111.
    Problem 3 • Volume(V): Approximately 1,178.1 cm³ Problem 4 • Volume (V): Approximately 251.2 ft³ Problem 5 • Volume (V): Approximately 226.2 cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 112.
    VOLUME WORD PROBLEMEXIT TICKET Problem 1 A cylindrical container has a radius of 6 cm and a height of 8 cm. What is its volume? Problem 2 If a cylindrical water tank is 10 feet tall and has a radius of 4 feet, how much water can it hold? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 113.
    Problem 3 A soupcan has a height of 12 cm and a radius of 5 cm. What is the volume of the can? Problem 4 A cylindrical vase has a diameter of 10 cm and a height of 15 cm. What is its volume? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 114.
    Answers: Problem 1 • Volume:Approximately 452.4 cm³ Problem 2 • Volume: Approximately 502.7 ft³ Problem 3 • Volume: Approximately 314.2 cm³ Problem 4 • Volume: Approximately 1178.1 cm³ hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 115.
    REFLECTION QUESTION How didparticipating in the volume- related activities enhance your understanding of calculating the volume of cylinders and its real-world applications? hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
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  • 117.
  • 118.
    hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com Question 1 A cylindricalcontainer has a radius of 3 cm and a height of 10 cm. What is its volume? A) 30π cm³ B) 90π cm³ C) 60π cm³ D) 15π cm³
  • 119.
    hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com Question 2 If acylindrical tank has a radius of 5 feet and a height of 8 feet, how much water can it hold? A) 100π ft³ B) 200π ft³ C) 250π ft³ D) 300π ft³
  • 120.
    hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com Question 3 A candlehas a diameter of 4 cm and a height of 10 cm. What is its volume? (Use π 3.14π 3.14) ≈ ≈ A) Approximately 50.24 cm³ B) Approximately 125.6 cm³ C) Approximately 31.4 cm³ D) Approximately 80 cm³
  • 121.
  • 122.
    REFERENCES • Mallari, K.G. (2024-2025). Lesson exemplar for mathematics grade 7: Quarter 2, Lesson 4 (Week 4). City College of San Fernando Pampanga • DepEd MATATAG Curriculum • Mallari, K. G. (2024-2025). Worksheet for mathematics grade 7: Quarter 2, Lesson 4 (Week 4). City College of San Fernando Pampanga hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com
  • 123.
    For more games,visit Hivessel.com Don't forget to support us in our socials below! hivesse l _hivesse l info.hivessel@gmail.co m Hivessel.com