A closed cylindrical tank contains 36pi 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?
If it is filled to half its capacity when placed on end, it will also be filled to half its capacity when placed on its side.
Since the height of the water is 4 feet when it is filled to half its capacity, the height of the tank is 8 feet.
I'm assuming that when the tank contains 36pi cubic feet of water, this only fills half the tank; therefore, the tank will hold 72pi cubic feet of water when completely filled.
Sice the volume of the tank is 72pi and the formula for volume is V = pi·r2·h
72pi = pi·r2·8
Divide both sides by 8pi: 9 = r2
The radius of the tank is 3 feet.and the diameter is 6 feet.
Half-ways, the water will reach 3 feet.