1. Volume of Prisms and Cylinders
8-5
Volume of Prisms and Cylinders
Warm Up
Problem of the Day
Lesson Presentation
Course 3

2. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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 ft2

3. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
Learn to find the volume of prisms and cylinders.

5. Insert Lesson Title Here
Course 3
8-5
Volume of Prisms and Cylinders
Insert Lesson Title Here
Vocabulary
cylinder
prism

6. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
A cylinder is a three-dimensional figure that has two congruent circular bases. A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms.

7. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
Triangular prism
Rectangular prism
Cylinder
Height
Height
Height
Base
Base
Base

8. VOLUME OF PRISMS AND CYLINDERS
Course 3
8-5
Volume of Prisms and Cylinders
VOLUME OF PRISMS AND CYLINDERS
Words
Numbers
Formula
Prism: The volume V of a prism is the area of the base B times the height h.
Cylinder: The volume of a cylinder is the area of the base B times the height h.
B = 2(5)
= 10 units2
V = Bh
V = 10(3)
= 30 units3
B =  (22)
V = Bh
= 4 units2
= (r2)h
V = (4)(6) = 24
 75.4 units3

9. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
Area is measured in square units. Volume is measured in cubic units.
Remember!

10. Additional Example 1A: Finding the Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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

11. Additional Example 1B: Finding the Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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
4 in.
V = Bh
Volume of a cylinder
12 in.
= 16 • 12
= 192  in3

12. Additional Example 1C: Finding the Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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
5 ft
V = Bh
Volume of a prism
= 15 • 7
= 105 ft3
7 ft
6 ft

13. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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

14. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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

15. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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

16. Additional Example 2A: Exploring the Effects of Changing Dimensions
Course 3
8-5
Volume of Prisms and Cylinders
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.

17. Additional Example 2B: Exploring the Effects of Changing Dimensions
Course 3
8-5
Volume of Prisms and Cylinders
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.

18. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
Check It Out: Example 2A
A box measures 5 in. by 3 in. by 7 in. Explain whether tripling 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.

19. Check It Out: Example 2A Continued
Course 3
8-5
Volume of Prisms and Cylinders
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.

20. Check It Out: Example 2A Continued
Course 3
8-5
Volume of Prisms and Cylinders
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.

21. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
Check It Out: Example 2B
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.

22. Check It Out: Example 2B Continued
Course 3
8-5
Volume of Prisms and Cylinders
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.

23. Additional Example 3: Music Application
Course 3
8-5
Volume of Prisms and Cylinders
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 in.2

24. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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 in.2

25. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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.

26. Volume of Prisms and Cylinders
Course 3
8-5
Volume of Prisms and Cylinders
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

27. Volume of Prisms and Cylinders Insert Lesson Title Here
Course 3
8-5
Volume of Prisms and Cylinders
Insert Lesson Title Here
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.