Question:
A reservoir in the shape of a right circular cylinder has a height of 84ft. If it to contain 79,200 L of water, find its radius.
Answer:
[tex]r = 3.26ft[/tex]
Step-by-step explanation:
Given
[tex]Volume = 79200L[/tex] ---- V
[tex]Height = 84ft[/tex] --- h
Required
Determine the radius
[tex]Volume = 79200L[/tex]
Convert volume to [tex]ft^3[/tex]
[tex]Volume = 79200 * 0.0353147ft^3[/tex]
[tex]Volume = 2796.9216ft^3[/tex]
The volume (V) of a cylinder is:
[tex]V = \pi r^2 h[/tex]
Substitute values for volume and height
[tex]2796.9216 = \pi * r^2 * 84[/tex]
Divide both sides by 84
[tex]33.2966857143 = \pi * r^2[/tex]
Take [tex]\pi[/tex] as 3.14
[tex]33.2966857143 = 3.14 * r^2[/tex]
Divide both sides by 3.14
[tex]10.604 = r^2[/tex]
[tex]r^2 = 10.604[/tex]
Take the square root of both sides
[tex]r = \sqrt{10.604[/tex]
[tex]r = 3.26ft[/tex]
Hence, the radius is 3.26 ft
