1. Volume of Prisms and Cylinders
6-6
Volume of Prisms and Cylinders
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. Learn to find the volume of prisms and cylinders.

3. Vocabulary
prism
cylinder

4. A prism is a three-dimensional figure named for the shape of its 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. A cylinder has two circular bases.

5. If all six faces of a rectangular prism are squares, it is a cube.
Remember!
Triangular prism
Rectangular prism
Cylinder
Height
Height
Height
Base
Base
Base

6. 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 = p(22)
V = Bh
= 4p units2
= (pr2)h
V = (4p)(6) = 24p
 75.4 units3

7. Area is measured in square units. Volume is measured in cubic units.
Helpful Hint

8. Additional Example 1A: Finding the Volume of Prisms and Cylinders
Find the volume of each figure to the nearest tenth.
A. 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

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

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

11. Try This: Example 1A
Find the volume of the figure to the nearest tenth.
A. 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

12. Try This: Example 1B
Find the volume of the figure to the nearest tenth.
B = p(82)
Area of base B.
8 cm
= 64p cm2
V = Bh
Volume of a cylinder
15 cm
= (64p)(15) = 960p
 3,014.4 cm3

13. Try This: Example 1C
Find the volume of the figure to the nearest tenth. C.
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

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 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 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.

16. Try This: 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.

17. Try This: 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 = (5)(3)(21) = 315 cm3
Tripling the height would triple the volume.

18. Try This: 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 = (5)(9)(7) = 315 cm3
Tripling the width would triple the volume.

19. Try This: 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.

20. Try This: 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 = 4 • 9 = 36 cm3
Tripling the height would triple the volume.

21. Additional Example 3: Construction Application
A section of an airport runway is a rectangular prism measuring 2 feet thick, 100 feet wide, and 1.5 miles long. What is the volume of material that was needed to build the runway?
length = 1.5 mi = 1.5(5280) ft
= 7920 ft
The volume of material needed to build the runway was 1,584,000 ft3.
width = 100 ft
height = 2 ft
V = 7920 • 100 • 2 ft3
= 1,584,000 ft3

22. Try This: Example 3
A cement truck has a capacity of 9 yards3 of concrete mix. How many truck loads of concrete to the nearest tenth would it take to pour a concrete slab 1 ft thick by 200 ft long by 100 ft wide?
B = 200(100)
= 20,000 ft2
V = 20,000(1)
= 20,000 ft3
20,000 27
 yd3
27 ft3 = 1 yd3
740.74 9
= 82.3 Truck loads

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 is 40,000 ft3.

24. Find the volume of the figure.
Try This: Example 4
Find the volume of the figure.
Volume of barn
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

25. Challenge:
A 6 cm section of plastic water pipe has inner diameter 12 cm and outer diameter 15 cm. Find the volume of the plastic pipe, not the hollow interior, to the nearest tenth.

26. Lesson Quiz
Find the volume of each figure to the nearest tenth. Use 3.14 for p.
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.