Water is poured into an initially empty hemispherical bowl of radius $12$ cm at a constant rate of

Question

Water is poured into an initially empty hemispherical bowl of radius $12$ cm at a constant rate of $6\pi$ $\text{cm}^3 / \text{s}$. The volume of water in the bowl, $V$ $\text{cm}^3$, is given by $V = \frac{1}{3} \pi x^2 (36 - x)$, where $x$ is the depth of water (in cm) directly below the centre. Find the time taken for $x$ to reach $6$ cm. Hence find the rate of change of $x$ at this instant.

Accepted Answer

(i) $60\text{ s}=1\text{ min}$ (ii) $\dfrac1{18}\text{ cm s}^{-1}$

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

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