Question

A spherical water tank holds 11,500 ft^3 of water. What is the diameter of the tank?​

Answer 1

The tank holding amount is volume. And the volume of a sphere is:

V = (4pir^3)/3

We know that radius is 1/2 of diameter:

r =d/2

So we rewrite our volume function:

V = 4/3(pi(d/2)^3)

We're given V = 11,500 so we have:

4/3(pi(d/2)^3) = 11500

Multiply each side by 3/4

4/3(3/4)(pi(d/2)^3) = 11,500*3/4

Simplify:

pi(d/2)^3 = 8625

Since pi = 3.1415926359, we divide each side by pi:

(d/2)^3 = 8625/3.1415926359

(d/2)^3 = 2745.42

Take the cube root of each side:

d/2 = 14.0224

Multiply through by 2:

d = 28.005