Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up Find each volume to the nearest tenth.
Use 3.14 for ?. 1. cylinder radius 6 m,
height 11 m
1,243.4 m3
2. rectangular prism length 10 cm, width
8.64 cm, height 12.9 cm
1,114.6 cm3
3. triangular prism base area 34 ft2,
height 18 ft
612 ft3
4. cylinder diameter 8 m, height 18 m
904.3 m3
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Problem of the Day When my age is divided by 2,
3, 4, or 6 there is always a remainder of 1, but
when it is divided by 7 there is no remainder.
How old am I?
49
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Sunshine State Standards
MA.7.G.2.1 Justify and apply formulas for volume
of pyramidsand cones. Also MA.7.G.2.2
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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 with the same
height and a congruent base.
The height of a pyramid is the
perpendicular distance from the pyramids base to
the vertex opposite the base.
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Additional Example 1A 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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Additional Example 1B 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.
Find the area of the triangular base.
B ½ 30 25 375
1 3
V
375 26
Substitute for B and h.
Multiply.
V 3250 ft3
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Check It Out Example 1A
Find the volume of each pyramid to the nearest
tenth. Estimate to check whether the answer is
reasonable.
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Check It Out Example 1A
1 3
1 3
(8)(7)(4)
V
Bh
V 74.7
about 74.7 ft3
Estimate.
1 3
V
54 4
72
The answer is reasonable
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Check It Out Example 1B
Find the volume of each pyramid to the nearest
tenth. Estimate to check whether the answer is
reasonable.
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Check It Out Example 1B Continued
1 3
1 3
B (9)(19) 85.5
V
Bh
1 3
(85.5)(12) 342
V
342 m
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Estimate.
1 3
V
84 12
336
The answer is reasonable
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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.
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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.
1 3
Estimate
? 150 yd3
The answer is reasonable.
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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.
1 3
Estimate
? 63 cm3
The answer is reasonable.
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Check It Out Example 2
Find the volume of the cone to the nearest tenth.
Use 3.14 for ?. Estimate to check whether the
answer is reasonable.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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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
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Lesson Quiz for Student Response Systems
1. Identify the volume of the prism. A. 576 ft3
B. 288 ft3 C. 96 ft3 D. 24 ft3
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Lesson Quiz for Student Response Systems
2. Identify the volume of cone to the nearest
tenth. Use 3.14 for ?. A. 4240.0 in3
B. 3815.1 in3 C. 1271.7 in3 D. 141.3
in3
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Lesson Quiz for Student Response Systems
3. Identify the volume of the pyramid. A. 1632
ft3 B. 544 ft3 C. 192 ft3 D. 27 ft3