Volume of Pyramids and Cones

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Volume of Pyramids and Cones
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
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• Warm Up
• 1. Find the volume of a rectangular prism that is
  4 in. tall, 16 in. wide, and 48 in deep.
• 2. A cylinder has a height of 4.2 m and a
  diameter of 0.6 m. To the nearest tenth of a
  cubic meter, what is the volume of the cylinder?
  Use 3.14 for p.
• 3. A triangular prisms base is an equilateral
  triangle. The sides of the equilateral triangle
  are 4 ft, and the height of the prism is 8 ft. To
  the nearest cubic foot, what is the volume of the
  prism?

3072 in3
1.2 m3
55.4 ft3
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Problem of the Day A ream of paper (500 sheets)
forms a rectangular prism 11 in. by 8.5 in. by 2
in. What is the volume of one sheet of paper?
0.374 in3
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Learn to find the volume of pyramids and cones.
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Vocabulary
pyramid cone
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A pyramid is named for the shape of its base. The
base is a polygon, and all of the other faces are
triangles. A cone has a circular base. The height
of a pyramid or cone is measured from the highest
point to the base along a perpendicular line.
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Additional Example 1A Finding the Volume of
Pyramids and Cones
Find the volume of the figure.
A.
V 28 cm3
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Additional Example 1B Finding the Volume of
Pyramids and Cones
Find the volume of the figure.
B.
B ?(32) 9? in2
V 30? ? 94.2 in3
Use 3.14 for ?.
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Additional Example 1C Finding the Volume of
Pyramids and Cones
Find the volume of the figure.
C.
B 14 6 84 m2
V 280 m3
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Try This Example 1A
Find the volume of the figure.
A.
7 in.
5 in.
7 in.
V ? 40.8 in3
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Try This Example 1B
Find the volume of the figure.
B.
B ?(32) 9? m2
7 m
3 m
V 21? ? 65.9 m3
Use 3.14 for ?.
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Try This Example 1C
Find the volume of the figure.
C.
B 4 4 16 ft2
8 ft
4 ft
4 ft
V ? 42.7 ft3
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Additional Example 2 Exploring the Effects of
Changing Dimensions
A cone has a radius of 3 ft. and a height of 4
ft. Explain whether tripling the height would
have the same effect on the volume of the cone as
tripling the radius.
When the height of the cone is tripled, the
volume is tripled. When the radius is tripled,
the volume becomes 9 times the original volume.
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Try This Example 2
A cone has a radius of 2 m and a height of 5 m.
Explain whether doubling the height would have
the same effect on the volume of the cone as
doubling the radius.
When the height of a cone is doubled, the volume
is doubled. When the radius is doubled, the
volume is 4 times the original volume.
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Additional Example 4 Social Studies Application
The Pyramid of Kukulcán in Mexico is a square
pyramid. Its height is 24 m and its base has 55 m
sides. Find the volume of the pyramid.
B 552 3025 m2
A bh
V 24,200 m3
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Try This Example 4
Find the volume of a pyramid with a height of 12
m and a base with 48 m sides.
B 482 2304 m2
A bh
V 9216 m3
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Lesson Quiz Part 1
Find the volume of each figure to the nearest
tenth. Use 3.14 for p.
1. the triangular pyramid
6.3 m3
2. the cone
78.5 in3
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Lesson Quiz Part 2
Find the volume of each figure to the nearest
tenth. Use 3.14 for p.
3. Explain whether tripling the height of a
square pyramid would triple the volume.
Yes the volume is one-third the product of the
base area and the height. So if you triple the
height, the product would be tripled.