Cylindrical Tank Height Increase

A cylindrical water tank has a radius of 3 feet and a height of 10 feet. It is initially filled with water to a height of 7 feet. If 5 cubic feet of water is added to the tank, what will be the new height of the water in the tank?

Recall that the volume of a cylinder is given by the formula:

$$ V = ext{Base Area} imes ext{Height} $$

where the Base Area can be calculated using the formula:

$$ ext{Base Area} = ext{Radius}^2 imes ext{π} $$