Question

A dairy farmer uses a storage silo that is in the shape of the right circular cylinder above. If the volume of the silo is $ 72\pi $ cubic yards, what is the diameter of the base of the cylinder in yards?

A. 5
B. 6
C. 7
D. 4

Answer 1

Hint: We are given that the silo is in the shape of a cylinder. And the volume of the cylinder is $ 72\pi $ cubic yards. The height of the cylinder is already given. To calculate the diameter we first need the radius. Equate the volume value with volume formula and substitute the height of the cylinder to find its radius.
Formula used:
Volume of a cylinder is $ \pi {r^2}h $ , where r is the base radius, h is the height of the cylinder and the value of $ \pi = \dfrac{{22}}{7} $

Complete step-by-step answer:
We are given that a dairy farmer uses a storage silo that is in the shape of the right circular cylinder above and the volume of the silo is $ 72\pi $ cubic yards.
We have to find the diameter of the base of the cylinder in yards.
A silo is a pit used to store the grains by farmers.
Volume of the cylinder (silo) is $ 72\pi $ cubic yards.
Volume of the cylinder can be calculated using $ \pi {r^2}h $ , we know the height of the cylinder as 8 yards.
 $
   \Rightarrow \pi {r^2}h = 72\pi \\
  h = 8yards \\
   \Rightarrow \pi {r^2} \times 8 = 72\pi \\
   \Rightarrow {r^2} = \dfrac{{72}}{8} \\
   \Rightarrow {r^2} = 9 \\
  \therefore r = 3yards \\
  $
The base radius of the cylinder is 3 yards.
Base diameter of the cylinder is twice of its base radius.
This means the base diameter is $ 2 \times 3 = 6 $ yards.

So, the correct answer is “Option B”.

Note: Volume of the cylinder is $ \pi {r^2}h $ , which can also be said as the product of the area of the base and its height. The base of a cylinder is always in circular shape and the area of the circle is $ \pi {r^2} $ . So $ \pi {r^2} $ times height will give $ \pi {r^2}h $ which will be the volume of the cylinder.