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

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. Problem of the Day
You are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another?
only 2

4. Sunshine State Standards
Prep for MA.8.G.5.1 …Convert units of measure between different measurement systems…and dimensions including…volume, and derived units to solve problems.
Rev MA.7.G.2.1, Rev MA.7.G.2.2

5. Vocabulary
volume 5

8. Area is measured in square units. Volume is measured in cubic units.
Remember!

9. Additional Example 1A: Finding the Volume of Prisms and Cylinders
Find the volume of each figure to the nearest tenth. Use 3.14 for .
a rectangular prism with base 2 cm by 5 cm and height 3 cm
B = 2 • 5 = 10 cm2
Area of base
V = Bh
Volume of a prism
= 10 • 3
= 30 cm3

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

11. Additional Example 1C: Finding the Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for .
B = • 6 • 5 = 15 ft2 1 2
Area of base
V = Bh
Volume of a prism
= 15 • 7
= 105 ft3

12. Check It Out: Example 1A
Find the volume of the figure to the nearest tenth. Use 3.14 for .
A rectangular prism with base 5 mm by 9 mm and height 6 mm.
B = 5 • 9 = 45 mm2
Area of base
V = Bh
Volume of prism
= 45 • 6
= 270 mm3

13. Check It Out: Example 1B
Find the volume of the figure to the nearest tenth. Use 3.14 for .
B =  (82)
Area of base
8 cm
= 64 cm2
V = Bh
Volume of a cylinder
15 cm
= (64)(15) = 960
 3,014.4 cm3

14. Check It Out: Example 1C
Find the volume of the figure to the nearest tenth. Use 3.14 for .
B = • 12 • 10 1 2
Area of base
10 ft
= 60 ft2
V = Bh
Volume of a prism
14 ft
= 60(14)
= 840 ft3
12 ft

15. Additional Example 2A: Exploring the Effects of Changing Dimensions
A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling 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.

16. 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 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 nine times the original.

17. Check It Out: Example 2
A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling 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.

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

19. 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)(6)2 • 4
Use 3 for p.
= (3)(36)(4)
≈ 432
The volume of the drum is approximately 432 in3.

20. Check It Out: Example 3
A drum company advertises a bass drum that is 9 inches high and 19 inches in diameter. Estimate the volume of the drum.
d = 19, h = 9
d 2
r = = = 9.5
V = (r2)h
Volume of a cylinder.
= (3)(9.5)2 • 9
Use 3 for .
= (3)(90.25)(9) ≈
The volume of the drum is approximately 2,437 in3.

21. 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 is 40,000 ft3.

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

23. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 23

24. 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.

25. Lesson Quiz for Student Response Systems
1. Identify the volume of the cylinder to the nearest tenth. Use 3.14 for .
A in3 B in3
C in3 D in3 25

26. Lesson Quiz for Student Response Systems
2. Identify the volume of the rectangular prism to the nearest tenth.
A. 338 m3 B. 390 m3
C. 364 m3 D m3 26

27. Lesson Quiz for Student Response Systems
3. Explain whether doubling the height of a rectangular prism will double the volume.
A. Yes; the volume would be doubled because you have to use the height to find the volume.
B. No; the volume would be tripled because you have to use height to find the volume.
C. No; the volume would be tripled because you have to use the square of the height to find the volume.
D. Yes; the volume would be doubled because you have to use the square of the height to find the volume. 27