Question

A grain silo is in the shape of a cylinder with a hemisphere top. They cylinder is 20 feet tall. The volume of the silo is 2106 cubic feet. Find the radius of the silo.

Answer 1

Answer:

The radius of the silo is 5.788 feet.

Step-by-step explanation:

Since the silo has the shape of a cylinder, then;

Volume of the silo = Volume of a cylinder = $\pi$$r^{2}$h

Where: r is the radius of the silo, and h is the height.

Given that: volume = 2106 cubic feet, and height = 20 feet.

Then,

2106 = $\frac{22}{7}$ x $r^{2}$ x 20

2106 = $\frac{440}{7}$$r^{2}$

2106 x 7 = 440$r^{2}$

14742 = 440$r^{2}$

$r^{2}$ = $\frac{14742}{440}$

$r^{2}$ = 33.5045

⇒ r = $\sqrt{33.5045}$

     = 5.78831

r = 5.788 feet

The radius of the silo is 5.788 feet.