1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up Find the area of each figure described. Use 3.14 for p.
1. a triangle with a base of 6 feet and a height of 3 feet
2. a circle with radius 5 in.
9 ft2
78.5 in2

3. California
Standards
MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
Also covered: MG2.4

4. Vocabulary
volume

5. The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.

6. Height Height Height Base Base Base Triangular prism Rectangular prism
Cylinder
Height
Height
Height
Base
Base
Base

8. Additional Example 1: Finding the Volume of Prisms and Cylinders
Find the volume of each figure to the nearest tenth. A.
B = 4 • 12 = 48 ft2
The base is a rectangle.
V = Bh
Volume of a prism
= 48 • 4
Substitute for B and h.
= 192 ft3
Multiply.

9. Additional Example 1: Finding the Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for . B.
The base is a circle.
B =  (42) = 16 in2
Volume of a cylinder
V = Bh
Substitute for B and h.
= 16 • 12
= 192  in3
Multiply.

10. Additional Example 1: Finding the Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for . C.
B = • 6 • 5 = 15 ft2 1 2
The base is a triangle.
V = Bh
Volume of a prism
7 ft
= 15 • 7
Substitute for B and h.
= 105 ft3
Multiply.

11. Find the volume of the figure to the nearest tenth. Use 3.14 for . A.
Check It Out! Example 1
Find the volume of the figure to the nearest tenth. Use 3.14 for . A.
10 in.
6 in.
3 in.
B = 6 • 3 = 18 in.2
The base is a rectangle.
V = Bh
Volume of prism
= 18 • 10
Substitute for B and h.
= 180 in3
Multiply.

12. Check It Out! Example 1
Find the volume of the figure to the nearest tenth. Use 3.14 for . B.
B =  (82)
The base is a circle.
8 cm
= 64 cm2
Volume of a cylinder
V = Bh
15 cm
Substitute for B and h.
= (64)(15) = 960
 3,014.4 cm3
Multiply.

13. Check It Out! Example 1
Find the volume of the figure to the nearest tenth. C.
B = • 12 • 10 1 2
The base is a triangle.
10 ft
= 60 ft2
V = Bh
Volume of a prism
14 ft
= 60(14)
Substitute for B and h.
= 840 ft3
Multiply.
12 ft

14. Additional Example 2A: Exploring the Effects of Changing Dimensions
A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling only the length, width, or height of the box would triple the amount of juice the box holds.
The original box has a volume of 24 in3. You could triple the volume to 72 in3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

15. Additional Example 2B: Exploring the Effects of Changing Dimensions
A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling only the height of the can would have the same effect on the volume as tripling the radius.
By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to 9 times the original volume.

16. Check It Out! Example 2A
A box measures 5 in. by 3 in. by 7 in. Explain whether tripling only the length, width, or height of the box would triple the volume of the box.
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (15)(3)(7) = 315 cm3
Tripling the length would triple the volume.

17. Check It Out! Example 2A Continued
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (5)(3)(21) = 315 cm3
Tripling the height would triple the volume.

18. Check It Out! Example 2A Continued
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (5)(9)(7) = 315 cm3
Tripling the width would triple the volume.

19. Check It Out! Example 2B
A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling only the radius or height of the cylinder would triple the amount of volume.
The original cylinder has a volume of 4 • 3 = 12 cm3.
V = 36 • 3 = 108 cm3
By tripling the radius, you would increase the volume nine times.

20. Check It Out! Example 2B Continued
The original cylinder has a volume of 4 • 3 = 12 cm3.
V = 4 • 9 = 36 cm3
Tripling the height would triple the volume.

21. Additional Example 3: Music Application
A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum.
d = 12, h = 4
d 2
r = = = 6
V = (r2)h
Volume of a cylinder
= (3.14)(6)2 • 4
Use 3.14 for p.
= (3.14)(36)(4)
= ≈ 452
The volume of the drum is approximately 452 in3.

22. Check It Out! Example 3
A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum.
d = 28, h = 12
d 2
r = = = 14
V = (r2)h
Volume of a cylinder
= (3.14)(14)2 • 12
Use 3.14 for .
= (3.14)(196)(12)
= ≈ 7,385
The volume of the drum is approximately 7,385 in3.

23. Additional Example 4: Finding the Volume of Composite Figures
Find the volume of the the barn.
Volume of barn
Volume of rectangular prism
Volume of triangular prism + =
V = (40)(50)(15) (40)(10)(50) 1 2
= 30, ,000
= 40,000 ft3
The volume of the barn is 40,000 ft3.

24. Find the volume of the play house.
Check It Out! Example 4
Find the volume of the play house.
Volume of house
Volume of rectangular prism
Volume of triangular prism + =
V = (8)(3)(4) (5)(8)(3) 1 2
5 ft =
V = 156 ft3
4 ft
The volume of the play house is 156 ft3.
8 ft
3 ft

25. Lesson Quiz
Find the volume of each figure to the nearest tenth. Use 3.14 for .
10 in. 1. 2. 3.
2 in.
12 in.
12 in.
10.7 in.
15 in.
3 in.
8.5 in.
942 in3
306 in3
160.5 in3
4. Explain whether doubling the radius of the cylinder above will double the volume.
No; the volume would be quadrupled because you have to use the square of the radius to find the volume.