Problem

Water is poured into a tank at a constant rate of $500\text{ cm}^3$ per second. The depth of water in the tank, $t$ seconds after filling starts, is $h\text{ cm}$. When the depth of water in the tank is $h\text{ cm}$, the volume, $V\text{ cm}^3$, of water in the tank is given by the formula $V=\frac{4}{3}(25+h)^3-62500$.

(a) Find the rate at which $h$ is increasing at the instant when $h=10\text{ cm}$.

(b) At another instant, the rate at which $h$ is increasing is $0.075\text{ cm}$ per second.

Find the value of $V$ at this instant.