Volume of Prisms and Cylinders

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8-5
Volume of Prisms and Cylinders
Warm Up
Problem of the Day
Lesson Presentation
Course 3
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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
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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
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Learn to find the volume of prisms and cylinders.
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Insert Lesson Title Here
Vocabulary
cylinder prism
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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.
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Rectangular prism
Cylinder
Triangular prism
Height
Height
Height
Base
Base
Base
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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
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(No Transcript)
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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
Volume of a prism
V Bh
10 3
30 cm3
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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.
Volume of a cylinder
V Bh
12 in.
16? 12
192? ? 602.9 in3
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Additional Example 1C Finding the Volume of
Prisms and Cylinders
Find the volume of the figure to the nearest
tenth. Use 3.14 for ?.
Area of base
5 ft
V Bh
Volume of a prism
15 7
105 ft3
7 ft
6 ft
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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
Volume of prism
V Bh
45 6
270 mm3
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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
Volume of a cylinder
V Bh
15 cm
(64?)(15) 960?
? 3,014.4 cm3
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Check It Out Example 1C
Find the volume of the figure to the nearest
tenth. Use 3.14 for ?.
Area of base
10 ft
60 ft2
Volume of a prism
V Bh
60(14)
14 ft
840 ft3
12 ft
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
12 2
r 6
Volume of a cylinder.
V (?r2)h
(3.14)(6)2 4
Use 3.14 for p.
(3.14)(36)(4)
452.16 452
The volume of the drum is approximately 452 in.2
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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
28 2
r 14
Volume of a cylinder.
V (?r2)h
(3.14)(14)2 12
Use 3.14 for ?.
(3.14)(196)(12)
7385.28 7,385
The volume of the drum is approximately 7,385 in.2
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Additional Example 4 Finding the Volume of
Composite Figures
Find the volume of the the barn.
30,000 10,000
40,000 ft3
The volume is 40,000 ft3.
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Check It Out Example 4
Find the volume of the house.
5 ft
96 60
4 ft
V 156 ft3
8 ft
3 ft
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Insert Lesson Title Here
Lesson Quiz
Find the volume of each figure to the nearest
tenth. Use 3.14 for ?.
10 in.
2 in.
1.
3.
2.
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.