Exercise
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Transcript of Exercise
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ExerciseIf a pyramid and a cone have bases with the same area and altitudes that are equal, are their surface areas equal?
no
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If a pyramid and a cone have bases with the same area and altitudes that are equal, are their volumes equal?
yes
Exercise
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In this text, what is the difference between h and H?
h = length of the altitude of a plane figure and H = length of the altitude of a solid figure.
Exercise
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What would the calculation of bhH give?
the volume of a triangular prism
12
Exercise
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h
wl
hwl
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Formula: Volume of a Pyramid or a ConeV = BH The volume of a pyramid or cone (V) is equal to one- third the area of the base (B) times
the height (H).
13
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Find the volume of the square pyramid.
= 256 cm3
V = BH13
= (82)(12)13
8 cm 8 cm
12 cm
Example 1
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Find the volume of the cone.
≈ 100.5 cm3
V = BH13
= p(42)(6)13
= 32p= 32(3.14)
6 cm
4 cm
Example 2
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What is the volume of a pyramid if its height is 10 units and its base is 8 units by 12 units?
320 units3
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What would happen to the volume of the pyramid in the previous question if its length were doubled?
The volume would be doubled.
Example
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What would happen to the volume if any single dimension were doubled?
Example
The volume would be doubled.
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What would happen if all the dimensions were doubled?
The volume would be multiplied by a factor of 23 = 8.
Example
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What is the volume of a square pyramid if each side of its base is 6 units and its height is 5 units?
60 units3
Example
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What would happen to the volume of the pyramid in the previous question if the sides of the square base were doubled?
The volume would be multiplied by a factor of 22 = 4.
Example
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Formula: Volume of a SphereV = pr3 The volume of a
sphere (V) is equal to the product of , p, and the radius cubed (r).
43
43
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Find the volume of a sphere with a diameter of 15 ft. to the nearest hundredth. Find the number of gallons it will hold. (1 ft.3 = 7.48 gal.)
r = = 7.5 ft.152
Example 3
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V = pr343
= p(7.53)43
= p(421.875)43
= p1,687.53
≈ 1,766.25 ft.3
Example 3
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≈ 13,212 gal.7.48(1,766.25)
Example 3
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Find the radius of a sphere with a volume of 288p m3.
V = pr343
pr3 = 288p43
pr3 = (288p)43
34 ( ) 3
4
Example 4
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pr3 = 216p
r3 = 216r = 6 m
Example 4
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What is the volume of a sphere with a radius of 6 units?
Example
904.32 units3
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A city needs a 10,000 m3 water tower for its increasing population. What should the radius be if the water tower is in the form of a sphere?
Example
13.37 m
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A grain storage bin is a steel cylinder with a conical top. One company markets a bin that is 18’ in diameter, 16’ high at the eaves, and 21’ high at the peak.
Exercise
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What is the maximum number of bushels of wheat (rounded to the nearest bushel) that can be stored in the bin? There are 0.8 bushels in one cubic foot.
Exercise
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V = pr2H + pr2H13
= 1,296p + 135p = 1,431p ft.3
= p(92)(16) + p(92)(5) 13
= 1,431p ft.3 0.8 bu.1 ft.3( )
≈ 3,595 bu.
Exercise