The document provides examples and explanations for calculating the volume of cylinders using the formula V = πr^2h. It includes step-by-step worked examples of finding the volume of cylinders with given radii and heights. It also features examples comparing the volumes of two cylinders and estimating volumes to the nearest unit. The lesson quiz at the end tests understanding of using the formula to calculate cylinder volumes and compare sizes.

1. Warm Up Lesson Presentation Problem of the Day Lesson Quizzes

2. Warm Up Find the volume of each figure described. 1. rectangular prism with length 12 cm, width 11 cm, and height 10 cm 2. triangular prism with height 11 cm and triangular base with base length 10.2 cm and height 6.4 cm 359.04 cm 3 1,320 cm 3

3. Problem of the Day The height of a box is half its width. The length is 12 in. longer than its width. If the volume of the box is 28 in 3 , what are the dimensions of the box? 1 in.  2 in.  14 in.

4. Preview of MA.7.G.2.1 Justify and apply formulas for…volumes of…cylinders. Sunshine State Standards

5. To find the volume of a cylinder, you can use the same method as you did for prisms: Multiply the area of the base by the height. volume of a cylinder = area of base  height The area of the circular base is  r 2 , so the formula is V = Bh =  r 2 h .

6. Additional Example 1A: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. r = 4 ft, h = 7 ft V =  r 2 h Write the formula. Replace  with 3.14 , r with 4, and h with 7. Multiply. V  351.68 V  3.14  4 2  7 The volume is about 352 ft 3 .

7. Additional Example 1B: Finding the Volume of a Cylinder V =  r 2 h d = 10 cm, h = 11 cm 10 cm ÷ 2 = 5 cm Find the radius. Write the formula. Replace  with 3.14 , r with 5, and h with 11. Multiply. V  863.5 V  3.14  5 2  11 The volume is about 864 cm 3 .

8. Additional Example 1C: Finding the Volume of a Cylinder V =  r 2 h r = in., h = 9 in. Find the radius. r = + 4 h 3 __ r = + 4 = 7 9 3 __ Substitute 9 for h. Write the formula. Replace  with 3.14 , r with 7, and h with 9. Multiply. V  1,384.74 V  3.14  7 2  9 The volume is about 1,385 in 3 . + 4 h 3 __

9. Check It Out: Example 1A Find the volume V of each cylinder to the nearest cubic unit. r = 6 ft, h = 5 ft V =  r 2 h Multiply. V  565.2 The volume is about 565 ft 3 . Write the formula. Replace  with 3.14 , r with 6, and h with 5. V  3.14  6 2  5

10. Check It Out: Example 1B d = 8 cm, h = 6 cm V =  r 2 h Multiply. V  301.44 8 cm ÷ 2 = 4 cm The volume is about 301 cm 3 . Find the radius. Write the formula. Replace  with 3.14 , r with 4, and h with 6. V  3.14  4 2  6

11. Check It Out: Example 1C r = + 5, h = 8 in. h 4 V =  r 2 h Multiply. V  1,230.88 The volume is about 1,231 in 3 . Find the radius. r = + 5 h 4 __ r = + 5 = 7 8 4 __ Substitute 8 for h. Write the formula. Replace  with 3.14 , r with 7, and h with 8. V  3.14  7 2  8

12. Additional Example 2A: Application Ali has a cylinder-shaped pencil holder with a 3 in. diameter and a height of 5 in. Scott has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 6 in. Estimate the volume of each cylinder to the nearest cubic inch. Ali’s pencil holder Write the formula. Replace  with 3.14 , r with 1.5, and h with 5. Multiply. V  35.325 3 in. ÷ 2 = 1.5 in. V  3.14  1.5 2  5 The volume of Ali’s pencil holder is about 35 in 3 . Find the radius. V =  r 2 h

13. Additional Example 2B: Application Scott’s pencil holder Write the formula. Multiply. 4 in. ÷ 2 = 2 in. The volume of Scott’s pencil holder is about 75 in 3 . Find the radius. V =  r 2 h Replace  with , r with 2, and h with 6. 22 7 __ V   2 2  6 22 7 __ V  = 75 528 7 ___ 3 7 __

14. Check It Out: Example 2A Sara has a cylinder-shaped sunglasses case with a 3 in. diameter and a height of 6 in. Ulysses has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 7 in. Estimate the volume of each cylinder to the nearest cubic inch. Sara’s sunglasses case Write the formula. Replace  with 3.14 , r with 1.5, and h with 6. Multiply. V  42.39 3 in. ÷ 2 = 1.5 in. V  3.14  1.5 2  6 The volume of Sara’s sunglasses case is about 42 in 3 . Find the radius. V =  r 2 h

15. Check It Out: Example 2B Ulysses’ pencil holder Write the formula. Multiply. 4 in. ÷ 2 = 2 in. The volume of Ulysses’ pencil holder is about 88 in 3 . Find the radius. V =  r 2 h Replace  with , r with 2, and h with 7. 22 7 __ V   2 2  7 22 7 __ V  88

16. Additional Example 3: Comparing Volumes of Cylinders Find which cylinder has the greater volume. Cylinder 1: Cylinder 2: V  3.14  1.5 2  12 V =  r 2 h V  84.78 cm 3 V  3.14  3 2  6 V =  r 2 h V  169.56 cm 3 Cylinder 2 has the greater volume because 169.56 cm 3 > 84.78 cm 3 .

17. Check It Out: Example 3 Find which cylinder has the greater volume. Cylinder 1: Cylinder 2: V  3.14  2.5 2  10 V =  r 2 h V  196.25 cm 3 V  3.14  2 2  4 V =  r 2 h V  50.24 cm 3 Cylinder 1 has the greater volume because 196.25 cm 3 > 50.24 cm 3 . 10 cm 2.5 cm 4 cm 4 cm

18. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. Lesson Quiz: Part I Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for  . cylinder b 1. radius = 9 ft, height = 4 ft 2. radius = 3.2 ft, height = 6 ft 3. Which cylinder has a greater volume? a. radius 5.6 ft and height 12 ft b. radius 9.1 ft and height 6 ft 1,560.14 ft 3 193 ft 3 1,017 ft 3 1,181.64 ft 3

20. 4. Jeff’s drum kit has two small drums. The first drum has a radius of 3 in. and a height of 14 in. The other drum has a radius of 4 in. and a height of 12 in. Estimate the volume of each cylinder to the nearest cubic inch. a. First drum b. Second drum Lesson Quiz: Part II about 396 in 3 about 603 in 3

21. 1. Identify the volume of a cylinder with a radius of 11 ft and a height of 5 ft to the nearest cubic unit. Use 3.14 for  A. 1,900 ft 3 B. 1,890 ft 3 C. 1,706 ft 3 D. 690 ft 3 Lesson Quiz for Student Response Systems

22. 2. Identify the volume of a cylinder with a radius of 4.3 ft and a height of 5 ft to the nearest cubic unit. Use 3.14 for  A. 338 ft 3 B. 305 ft 3 C. 297 ft 3 D. 290 ft 3 Lesson Quiz for Student Response Systems

23. 3. A mechanic uses two small iron tubes. The first tube has a radius of 4 in. and a height of 12 in. The other tube has radius of 5 in. and a height of 10 in. Estimate the volume of each tube to the nearest cubic inch. A. first tube: about 942 in 3 ; second tube: about 502 in 3 B. first tube: about 603 in 3 ; second tube: about 502 in 3 C. first tube: about 942 in 3 ; second tube: about 785 in 3 D. first tube: about 603 in 3 ; second tube: about 785 in 3 Lesson Quiz for Student Response Systems