Volume of Prisms and Cylinders
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Volume of Prisms and Cylinders
Warm Up
Find the area of each figure described. Use 3.14 for .
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
Volume of Prisms and Cylinders
Problem of the DayYou 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
Volume of Prisms and Cylinders
Learn to find the volume of prisms and cylinders.
Volume of Prisms and Cylinders
Volume of Prisms and Cylinders
Volume of Prisms and Cylinders
Area is measured in square units. Volume is measured in cubic units.
Remember!
Volume of Prisms and Cylinders
Find the volume of each figure to the nearest tenth. Use 3.14 for .
Additional Example 1A: Finding the Volume of Prisms and Cylinders
a rectangular prism with base 2 cm by 5 cm and height 3 cm
= 30 cm3
B = 2 • 5 = 10 cm2
V = Bh
= 10 • 3
Area of base
Volume of a prism
Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for .
4 in.
12 in.
= 192 602.9 in3
B = (42) = 16 in2
V = Bh
= 16 • 12
Additional Example 1B: Finding the Volume of Prisms and Cylinders
Area of baseVolume of a cylinder
Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for .
5 ft
7 ft
6 ft
V = Bh= 15 • 7= 105 ft3
B = • 6 • 5 = 15 ft212
Additional Example 1C: Finding the Volume of Prisms and Cylinders
Area of base
Volume of a prism
Volume of Prisms and Cylinders
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.
= 270 mm3
B = 5 • 9 = 45 mm2
V = Bh
= 45 • 6
Area of base
Volume of prism
Check It Out: Example 1A
Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for .
8 cm
15 cm
B = (82)= 64 cm2
= (64)(15) = 960
3,014.4 cm3
Check It Out: Example 1B
Area of base
Volume of a cylinderV = Bh
Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for .
10 ft
14 ft
12 ft
= 60 ft2
= 60(14)= 840 ft3
Check It Out: Example 1C
Area of base
Volume of a prism
B = • 12 • 10 12
V = Bh
Volume of Prisms and Cylinders
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.
Additional Example 2A: Exploring the Effects of Changing Dimensions
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.
Volume of Prisms and Cylinders
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.
Additional Example 2B: Exploring the Effects of Changing Dimensions
By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.
Volume of Prisms and Cylinders
By tripling the radius, you would increase the volume nine times.
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.
Check It Out: Example 2
V = 36 • 3 = 108 cm3
The original cylinder has a volume of 4 • 3 = 12 cm3.
Volume of Prisms and CylindersCheck It Out: Example 2 Continued
Tripling the height would triple the volume.
V = 4 • 9 = 36 cm3
The original cylinder has a volume of 4 • 3 = 12 cm3.
Volume of Prisms and Cylinders
A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum.
Additional Example 3: Music Application
d = 12, h = 4r = = = 6
Volume of a cylinder.
d 2V = (r2)h
12 2
= (3.14)(6)2 • 4 = (3.14)(36)(4) = 452.16 ≈ 452
Use 3.14 for .
The volume of the drum is approximately 452 in3.
Volume of Prisms and Cylinders
A drum company advertises a bass drum that is 9 inches high and 19 inches in diameter. Estimate the volume of the drum.
Check It Out: Example 3
d = 19, h = 9r = = = 9.5
Volume of a cylinder.
d 2V = (r2)h
19 2
= (3.14)(9.5)2 • 9 = (3.14)(90.25)(9) = 2550.465 ≈ 2550
Use 3.14 for .
The volume of the drum is approximately 2,550 in3.
Volume of Prisms and Cylinders
Find the volume of the the barn.
Volume of barn
Volume of rectangular
prism
Volume of triangular
prism+=
= 30,000 + 10,000V = (40)(50)(15) + (40)(10)(50)1
2
= 40,000 ft3
The volume is 40,000 ft3.
Additional Example 4: Finding the Volume of Composite Figures
Volume of Prisms and CylindersCheck It Out: Example 4
Find the volume of the house.
3 ft
4 ft
8 ft
5 ft
= (8)(3)(4) + (5)(8)(3)12
= 96 + 60
V = 156 ft3
Volume of house
Volume of rectangular
prism
Volume of triangular
prism+=
Volume of Prisms and Cylinders
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
Volume of Prisms and CylindersLesson Quiz
Find the volume of each figure to the nearest tenth. Use 3.14 for .
306 in3942 in3 160.5 in3
No; the volume would be quadrupled because you have to use the square of the radius to find the volume.
10 in.
8.5 in.3 in.
12 in.12 in.2 in.
15 in.10.7 in.
1. 3.2.
4. Explain whether doubling the radius of the cylinder above will double the volume.
Volume of Prisms and Cylinders
1. Identify the volume of the cylinder to the nearest tenth. Use 3.14 for .
A. 1099 in3 B. 1582.6 in3
C. 1356.5 in3 D. 1846.3 in3
Lesson Quiz for Student Response Systems
Volume of Prisms and Cylinders
2. Identify the volume of the rectangular prism to the nearest tenth.
A. 338 m3 B. 390 m3
C. 364 m3 D. 422.5 m3
Lesson Quiz for Student Response Systems
Volume of Prisms and Cylinders
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.
Lesson Quiz for Student Response Systems