Problem Solving

A closed cylindrical tank contains 36*pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 2 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

Correct Answer is: B

Please explain how to solve this question.

Note that, as the tank is filled to half of its capacity,

• # When the tank is placed upright on its circular base on level ground, the height of the water must be half of the height of the tank.
  # When the tank is placed on its side on level ground, the height of the water must be equal to the radius of the tank.

Basically we need to determine the radius of the circular base of the cylinder.

So, half height of the tank, h/2 = 2 cm
Half volume of the cylinder = πr²h/2 = 2πr² = 36π
So, r² = 18 ---> r = 3√2

Answer could B, i.e. r = 3 only if "When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet"