Water is poured into an inverted cone (as shown in the diagram) of base radius $6$ cm and height o

Question

Water is poured into an inverted cone (as shown in the diagram) of base radius $6$ cm and height of $10$ cm at a constant rate of $3\text{ cm}^3 / \text{s}$. The container is initially empty. Show that the volume of water, $V\text{ cm}^3$, in the cone at any time is given by $V = \frac{3 \pi x^3}{25}$, where $x$ is the height of water (cm) in the cone. Hence find the rate of change of $x$ when the radius of water is $3$ cm. Leave your answer in terms of $\pi$.

Accepted Answer

(i) $V=\dfrac{3\pi x^3}{25}$ (ii) $\dfrac{1}{3\pi}\text{ cm s}^{-1}$

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

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