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. $9$

Answer 1

The correct option is B $3$

Since the cylinder is half full, it will be filled to half its height, whether it is upright or on its side.When the cylinder is on its side, half its height is equal to its radius.

Using the information about the volume of water in the upright cylinder, solve for this radius to determine the height of the water when the cylinder is on its side.

$V=\pi r^{2}hvolume=\left(\pi \right)\left(radiu{s}^2\right)\left(height\right)$

$36\pi =\pi r^{2}h$ known volume of water is $36\pi$

$36=r^2\left(4\right)$ substitute $4$ for $h$; divide both sides by $\pi$

$9=r^2$ solve for $r$

$3=r$ $radius=height$ of the water in the cylinder on its side

The correct answer is B.