Learn to find the volume of prisms and Pyramids

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Learn to find the volume of prisms and Pyramids
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Vocabulary
volume
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Any three-dimensional figure can be filled
completely with congruent cubes and parts of
cubes. The volume of a three-dimensional figure
is the number of cubes it can hold. Each cube
represents a unit of measure called a cubic unit.
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Additional Example 1 Using Cubes to Find the
Volume of a Rectangular Prism
Find how many cubes the prism holds. Then give
the prisms volume.
You can find the volume of this prism by counting
how many cubes tall, long, and wide the prism is
and then multiplying.
1 4 3 12
There are 12 cubes in the prism, so the volume is
12 cubic units.
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To find a prisms volume, multiply its length by
its width by its height.
4 cm 3 cm 1cm 12 cm3
length width height volume
area of base
height volume
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Reading Math
Any unit of measurement with an exponent of 3 is
a cubic unit. For example, cm3 means cubic
centimeter and in3 means cubic inch.
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Check It Out Example 1
Find how many cubes the prism holds. Then give
the prisms volume.
You can find the volume of this prism by counting
how many cubes tall, long, and wide the prism is
and then multiplying.
2 4 3 24
There are 24 cubes in the prism, so the volume is
24 cubic units.
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The volume of a rectangular prism is the area of
its base times its height. This formula can be
used to find the volume of any prism.
VOLUME OF A PRISM
The volume V of a prism is the area of its base B times its height h. V Bh
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Additional Example 2A Using a Formula to Find
the Volume of a Prism
Find the volume of the prism.
4 ft
4 ft
12 ft
V Bh
Use the formula.
The bases are rectangles.
The area of each rectangular base is 12 4 48
V 48 4
Substitute for B and h.
Multiply.
V 192
The volume of the prism is 192 ft3.
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Additional Example 2B Using a Formula to Find
the Volume of a Prism
Find the volume of the prism.
V Bh
Use the formula.
The base is a triangle.
V 6 6
Substitute for B and h.
Multiply.
V 36
The volume of the prism is 36 cm3.
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Check It Out Example 2A
Find the volume of the prism.
6 ft
6 ft
8 ft
V Bh
Use the formula.
The bases are rectangles.
The area of each rectangular base is 8 6 48
V 48 6
Substitute for B and h.
Multiply.
V 288
The volume to the nearest tenth is 288 ft3.
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Check It Out Example 2B
Find the volume of the prism.
5 in
4 in.
1.5 in.
V Bh
Use the formula.
The base is a triangle.
V 3.75 4
Substitute for B and h.
Multiply.
V 15
The volume of the prism is 15 in3.
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In fact, the volume of a pyramid is exactly
one-third the volume of a prism if they have the
same height and same-size base.
The height of a pyramid is the
perpendicular distance from the pyramids base to
its vertex.
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Additional Example 1 Finding the Volume of a
Rectangular Pyramid
Find the volume of the pyramid to the nearest
tenth. Estimate to check whether the answer is
reasonable.
1 3
V
Bh
Use the formula.
4 ft
Find the area of the rectangular base.
B 5 7 35
1 3
V
35 4
Substitute for B and h.
7 ft
5 ft
Multiply.
V 46.7 ft3
1 3
V
Round the measurements.
30 5
Estimate
The answer is reasonable.
V 50 ft3
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Check It Out Example 1
Find the volume of the pyramid to the nearest
tenth. Estimate to check whether the answer is
reasonable.
1 3
V
Bh
Use the formula.
4 ft
Find the area of the rectangular base.
B 8 7 56
1 3
V
56 4
Substitute for B and h.
7 ft
8 ft
Multiply.
V 74.7 ft3
1 3
V
Estimate
Round the measurements.
60 4
The answer is reasonable.
V 80 ft3
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Lesson Quiz Part I
Find how many cubes the prism holds. Then give
the prisms volume.
1.
2.
48 cubic units
792 cm3