Question

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 120 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

Answer 1

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 : r = 120 feet

Height of roof ( cone ) h = 25 feet

Total height of silo = 130 feet

Then , height of cylindrical part H= 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. $5,127,079\ ft^3$.