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 = [tex]\pi[/tex][tex]r^{2}[/tex]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 = [tex]\frac{22}{7}[/tex] x [tex]r^{2}[/tex] x 20
2106 = [tex]\frac{440}{7}[/tex][tex]r^{2}[/tex]
2106 x 7 = 440[tex]r^{2}[/tex]
14742 = 440[tex]r^{2}[/tex]
[tex]r^{2}[/tex] = [tex]\frac{14742}{440}[/tex]
[tex]r^{2}[/tex] = 33.5045
⇒ r = [tex]\sqrt{33.5045}[/tex]
= 5.78831
r = 5.788 feet
The radius of the silo is 5.788 feet.
