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Hatshy [7]
3 years ago
6

A silo is a composite of a cylindrical tower with a cone for a roof. Find the volume of the silo if the radius of the base is 12

0 feet, the height of the roof is 25 feet, and the height of the entire silo is 130 feet.
A. 4,750,088 ft^3
B. 376,991 ft^3
C. 5,127,079 ft^3
D. 4,373,097 ft^3
Mathematics
1 answer:
goblinko [34]3 years ago
4 0

Answer: C. 5,127,079 ft^3

Step-by-step explanation:

Given : A silo is a composite of a cylindrical tower with a cone for a roof.

Base radius : <em>r</em> = 120 feet

Height of roof ( cone ) <em>h</em> = 25 feet

Total height of silo = 130 feet

Then , height of cylindrical part <em>H</em>= 130 - 25 = 105 feet

Volume of silo = volume of cylinder +volume of cone

=\pi r^2H+\dfrac{1}{3}\pi r^2h

=\pi r^2(H+\dfrac{h}{3})

Substitute corresponding values

=(3.14159265359)(120)^2(105+\dfrac{25}{3})\\\\=(3.14159265359)(14400)(\dfrac{340}{3})\\\\=5127079.21066\approx5127079\ ft^3

Hence, the correct answer is C. 5,127,079\ ft^3.

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