8-5 volume of prisms and cylinders course 3 warm up warm up problem of the day problem of the day...
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8-5 Volume of Prisms and Cylinders
Course 3
Warm Up
Problem of the Day
Lesson Presentation
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.
Course 3
8-5 Volume of Prisms and Cylinders
9 ft2
78.5 ft2
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
Course 3
8-5 Volume of Prisms and Cylinders
Learn to find the volume of prisms and cylinders.
Course 3
8-5 Volume of Prisms and Cylinders
Vocabulary
cylinder
prism
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Course 3
8-5 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.
Course 3
8-5 Volume of Prisms and Cylinders
Height
Triangular prism
Rectangular prism
Cylinder
Base
Height
Base
Height
Base
Course 3
8-5 Volume of Prisms and Cylinders
VOLUME OF PRISMS AND CYLINDERSWords 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 = 10(3)
= 30 units3
B = (22)= 4 units2
V = (4)(6) = 24 75.4 units3
V = Bh
V = Bh
= (r2)h
Course 3
8-5 Volume of Prisms and Cylinders
Area is measured in square units. Volume is measured in cubic units.
Remember!
Find the volume of each figure to the nearest tenth. Use 3.14 for .
Additional Example 1A: Finding the Volume of Prisms and Cylinders
Course 3
8-5 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
Find the volume of the figure to the nearest tenth. Use 3.14 for .
Course 3
8-5 Volume of Prisms and Cylinders
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 base
Volume of a cylinder
Find the volume of the figure to the nearest tenth. Use 3.14 for .
Course 3
8-5 Volume of Prisms and Cylinders
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
Find the volume of the figure to the nearest tenth. Use 3.14 for .
Course 3
8-5 Volume of Prisms and Cylinders
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
Find the volume of the figure to the nearest tenth. Use 3.14 for .
Course 3
8-5 Volume of Prisms and Cylinders
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
Find the volume of the figure to the nearest tenth. Use 3.14 for .
Course 3
8-5 Volume of Prisms and Cylinders
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
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
Course 3
8-5 Volume of Prisms and Cylinders
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.
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
Course 3
8-5 Volume of Prisms and Cylinders
By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.
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.
Check It Out: Example 2A
Course 3
8-5 Volume of Prisms and Cylinders
Tripling the length would triple the volume.
V = (15)(3)(7) = 315 cm3
The original box has a volume of (5)(3)(7) = 105 cm3.
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.
Tripling the height would triple the volume.
V = (5)(3)(21) = 315 cm3
Course 3
8-5 Volume of Prisms and Cylinders
Check It Out: Example 2A Continued
Tripling the width would triple the volume.
V = (5)(9)(7) = 315 cm3
The original box has a volume of (5)(3)(7) = 105 cm3.
Course 3
8-5 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 2B
V = 36 • 3 = 108 cm3
The original cylinder has a volume of 4 • 3 = 12 cm3.
Check It Out: Example 2B Continued
Course 3
8-5 Volume of Prisms and Cylinders
Tripling the height would triple the volume.
V = 4 • 9 = 36 cm3
The original cylinder has a volume of 4 • 3 = 12 cm3.
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
Course 3
8-5 Volume of Prisms and Cylinders
d = 12, h = 4
r = = = 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 in.2
A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum.
Check It Out: Example 3
Course 3
8-5 Volume of Prisms and Cylinders
d = 28, h = 12
r = = = 14
Volume of a cylinder.
d 2V = (r2)h
28 2
= (3.14)(14)2 • 12
= (3.14)(196)(12)
= 7385.28 ≈ 7,385
Use 3.14 for .
The volume of the drum is approximately 7,385 in.2
Course 3
8-5 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 + 10,000
V = (40)(50)(15) + (40)(10)(50)12
= 40,000 ft3
The volume is 40,000 ft3.
Additional Example 4: Finding the Volume of Composite Figures
Check It Out: Example 4
Course 3
8-5 Volume of Prisms and Cylinders
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+=
Lesson QuizFind the volume of each figure to the nearest tenth. Use 3.14 for .
306 in3942 in3
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160.5 in3
No; the volume would be quadrupled because you have to use the square of the radius to find the volume.
Course 3
8-5 Volume of Prisms and Cylinders
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.