Question

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 4 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

Hint:

In problems involving volume and geometry, relate known quantities to the formula for volume and solve step by step.

Answer 1

The Correct Option is A

Step 1: Calculate the radius and height of the tank.
The tank has a volume of \( 36\pi \) cubic feet, which is half of its capacity, so its full capacity is \( 72\pi \) cubic feet. The volume of a cylinder is given by: \[ V = \pi r^2 h \] Where \( r \) is the radius and \( h \) is the height. We know that the height of the water when the tank is upright is 4 feet. Solving for the radius: \[ 72\pi = \pi r^2 \times 4 \implies r^2 = 18 \implies r = \sqrt{18} \] Step 2: Find the height when the tank is placed on its side.
When the tank is placed on its side, the water will rise up to the height of 2 feet. So, the height of the surface of the water above the ground is 2 feet. \[ \boxed{2} \]