This document provides information and examples about finding the volume of cylinders and cones. It includes: 1. The formula for finding the volume of a cylinder which is V = πr^2h. 2. The formula for finding the volume of a cone which is V = (1/3)πr^2h. 3. Several examples of using these formulas to calculate the volume of cylinders and cones based on given radius and height measurements.

1. Course 3, Lesson 8-2
Find the volume of the cylinder. Round to the nearest tenth.
1. 2.
3. A water trough for a herd of cattle is a cylinder with a radius of 2.2
meters and a height of 1.1 meters. What is the volume of water that
can be held in the trough?
4. A cylindrical canning jar has a diameter of 3.2 inches and a height of
5.2 inches. What is the approximate volume of the canning jar?

2. Course 3, Lesson 8-2
ANSWERS
1. 6.4 yd3
2. 138.2 cm3
3. 16.7 m3
4. 41.8 in3

3. WHY are formulas important
in math and science?
Geometry
Course 3, Lesson 8-2

4. Course 3, Lesson 8-2 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
Geometry
• 8.G.9
Know the formulas for the volumes of cones, cylinders, and spheres
and use them to solve real-world and mathematical problems.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

5. To
• find the volume of a cone
Course 3, Lesson 8-2
Geometry

6. • cone
Course 3, Lesson 8-2
Geometry

7. Course 3, Lesson 8-2
Geometry
Words The volume V of a cone with radius r is one third the
area of the base B times the height h.
Model
Symbols V = Bh or V = πr2h
1
3
1
3

8. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. Find the volume of the cone. Round to the nearest tenth.
V = πr2h Volume of a cone
V = • π • 32 • 6 r = 3, h = 6
V ≈ 56.5 Simplify
The volume is about 56.5 cubic inches.

9. Answer
Need Another Example?
Find the volume of the cone. Round to the
nearest tenth.
26.2 in3

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. A cone-shaped paper cup is filled with water. The height of the cup
is 10 centimeters and the diameter is 8 centimeters. What is the
volume of the paper cup? Round to the nearest tenth.
V = πr2h Volume of a cone
r = 4, h = 10
V ≈ 167.6 Simplify
The volume of the paper cup is about 167.6 cubic centimeters.
V = • π • 42 • 10

11. Answer
Need Another Example?
A cone-shaped vase has a height of 15 centimeters
and a diameter of 8 centimeters. What is the volume
of the vase? Round to the nearest tenth.
251.3 cm3

12. 1
Need Another Example?
2
3
Step-by-Step Example
3. Find the volume of the solid.
Round to the nearest tenth.
Find the volume of the cylinder.
Volume of a cylinder
So, the volume of the solid is about 201.1 + 83.8 or
284.9 cubic feet.
Find the volume of the cone.
Volume of a cone
V = π • 42 • 4
V = π • 16 • 4
V ≈ 201.1
V = πr2h
r = 4, h = 4
Simplify
Simplify
V = πr2h
V = π • 42 • 5
V = π • 16 • 5
V ≈ 83.8
r = 4, h = 5
Simplify
Simplify

13. Answer
Need Another Example?
Find the volume of the solid. Round to the nearest
tenth.
318.3 in3

14. How did what you learned
today help you answer the
WHY are formulas important
in math and science?
Course 3, Lesson 8-2
Geometry

15. How did what you learned
today help you answer the
WHY are formulas important
in math and science?
Course 3, Lesson 8-2
Geometry
Sample answers:
• The formula is used to find the volume of a
cone.
• When having a cylinder and a cone as a composite
solid, the formulas and can be used to
find the volume of the composite figure.
V r h 21
3
2V r h V r h 21
3

16. How did the previous lesson
on finding the volume of
a cylinder help you with
finding the volume of a cone?
Course 3, Lesson 8-2
Ratios and Proportional RelationshipsFunctionsGeometry