Chapter 12
12.4
Volume of Prisms and Cylinders
Volume of a Cylinder
•
Theorem 12.8: Volume of a Cylinder
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The volume V of a Cylinder is V = Bh = r2h, where
B is the area of the base (a circle), h is the height, and
r is the radius.
1. Area of Base: A = (4)2
•
Base is a circle
2. Height: h = 11
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Distance between bases
3. Volume: V = (16)11 = 176 in3
Find the volume of the following
cylinders
1. Base is a circle with radius 8.1
B = (8.1)2 = 65.61
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2. h = 10
3. V = (65.61)10 = 656.1
1. Base is a circle with radius 3
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B = (3)2 = 9
2. h = 12
3. V = (9)12 = 108
Find the Volume of the Cylinder
1. Base is a circle with radius 4
•
B = (4)2 = 16
2. h = 9.5
3. V = (16)9.5 = 152
Solve for the variable using the given
measurements. The prisms and
cylinders are right
1. The solid is a right rectangular prism
•
V = Bh, B = 15(5), h = x
2. Fill in the information
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525 = 15(5)x
3. Solve for x
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x=7
Solve for the variable using the given
measurements. The prisms and
cylinders are right
1. The solid is a right cylinder
•
V = Bh = r2h, r = 8, h = x
2. Fill in the information
•
2420 = (8)2x
3. Solve for x
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x  12
Solve for the variable using the given
measurements. The prisms and
cylinders are right.
1. The solid is a right triangular prism
•
V = Bh, B is the area of the triangle
2. Fill in the information
•
455 = ½(10)(14)x
3. Solve for x
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x = 6.5
Make a sketch of the solid and find its
volume
13. A prism has a square base with 5 foot sides and a
height of 2.5 feet.
1. The solid is a square based prism
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V = Bh, B = 52
2. Find the Height
5 ft
2.5 ft
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h = 2.5
3. Substitute and find the volume
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V = 52(2.5) = 62.5 ft3
Make a sketch of the solid and
find its volume
14. A cylinder has a diameter of 23 inches and a height of 16 inches.
1. Base is a circle with radius 11.5
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16
B = (11.5)2 = 132.25
2. h = 16
3. V = (132.25)16 = 2116 in3
11.5
15. Pillars How much plaster of paris is needed to
make four miniature pillars for a model home if the
pillars are regular hexagonal prisms with a height of
12 in. and base edges of 2 in.?
1. Base is a hexagon with s = 2
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a = 3
• B
1
2
ans 
1
2
 3 6 2   6
3
2. h = 12
3. V = (6 3)12 = 723 in3
4. Since there are 4 pillars you need to
multiply by 4
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Amount = 4(723) = 2883 in3
Homework #65
Pg 747 – 749 16-18, 22-24, 26,
28-33, 39-49, 51-60