Question

A half-filled cylindrical water tank has a water level of 20 feet high. The tank can hold 6000 cubic feet of water. Find the diameter of the tank in feet to the nearest tenth.

Answer 1

d = 13.8 feet

Explanation:

Because we are talking about cubic feet of water, we need the formula for the VOLUME of a cylinder. That formula is

`V=\pi r^2h`

We will use 3.141592654 for pi; if the tank HALF filled with water is at 20 feet, then the height of the tank is 40 feet, so h = 40; and the volume it can hold in total is 6000 cubic feet. Filling in then gives us:

`6000=(3.141592654)(r^2)(40)`

Simplify on the right to get

`6000=125.6637061r^2`

Divide both sides by 125.6637061 to get that

`r^2=47.74648294`

Taking the square root of both sides gives you

r = 6.90988299

But the diameter is twice the radius, so multiply that r value by 2 to get that the diameter to the nearest tenth of a foot is 13.8