Answer:
d = 13.8 feet
Step-by-step explanation:
Because we are talking about cubic feet of water, we need the formula for the VOLUME of a cylinder. That formula is
[tex]V=\pi r^2h[/tex]
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:
[tex]6000=(3.141592654)(r^2)(40)[/tex]
Simplify on the right to get
[tex]6000=125.6637061r^2[/tex]
Divide both sides by 125.6637061 to get that
[tex]r^2=47.74648294[/tex]
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
