Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Learn to find the volume of pyramids and cones.
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Suppose you have a square-pyramid-shaped
container and a square-prism-shaped container,
and the bases and heights are the same size. If
you pour sand from the pyramid into the prism, it
appears that the prism holds three times as much
sand as the pyramid.
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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.
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

Round the measurements.
The answer is reasonable.
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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
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The volume of a cone is one-third the volume of a
cylinder with the same height and a congruent
base. The height of a cone is the perpendicular
distance from the cones base to its vertex.
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Additional Example 2A Finding the Volume of a
Cone
Find the volume of the cone to the nearest tenth.
Use 3.14 for ?. Estimate to check whether the
answer is reasonable.
1 3
Use the formula. The base is a circle so B ?
r2 ? 3.14 52 ? 78.5.
Bh
V
1 3
Substitute for B and h.
78.5 6
V ?
V ? 157 yd3
Multiply.
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Additional Example 2B Finding the Volume of a
Cone
Find the volume of the cone to the nearest tenth.
Use 3.14 for ?. Estimate to check whether the
answer is reasonable.
1 3
Use the formula. The base is a circle so B ?
r2 ? 3.14 32 ? 28.26.
Bh
V
1 3
Substitute for B and h.
28.26 7
V ?
V ? 65.9 cm3
Multiply.
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Check It Out Example 2A
Find the volume of the cone to the nearest tenth.
Use 3.14 for ?.
1 3
Use the formula. The base is a circle so B ?
r2 ? 3.14 32 ? 12.56.
Bh
V
1 3
Substitute for B and h.
12.56 3
V ?
V 12.6 yd3
Multiply.
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Check It Out Example 2B
Find the volume of the cone to the nearest tenth.
Use 3.14 for ?. Estimate to check whether the
answer is reasonable.
1 3
Bh
V
1 3
Substitute for B and h.
12.56 7
V ?
V ? 29.3 cm3
Multiply.
1 3
Estimate
? 28 cm3
The answer is reasonable.
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Lesson Quiz
Find the volume of each pyramid or cone to the
nearest tenth. Use 3.14 for ?. Estimate to check
whether the answer is reasonable.
1. 2.
80 ft3
301.4 yd3
3.
252 ft3