(a)[3]
Find the rate at which $h$ is increasing at the instant when $h = 10\,\text{cm}$.
(b)[3]
At a different instant, the rate at which $h$ is increasing is $0.075\,\text{cm}$ per second. Find the value of $V$ at this instant.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
Water enters a tank at a steady rate of $500\,\text{cm}^3$ per second. The water depth in the tank is $h$ cm, measured $t$ seconds after filling begins. When the water depth is $h$ cm, the volume, $V\,\text{cm}^3$, of water in the tank is given by the formula $V = \dfrac{4}{3}(25 + h)^3 - \dfrac{62500}{3}$.
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