A hemispherical water dispenser has a radius $8$ cm and is initially full of water. The water is d

Question

A hemispherical water dispenser has a radius $8$ cm and is initially full of water. The water is dispensed at a constant rate into an inverted conical cup that has a base radius $8$ cm and height $16$ cm and is initially empty. The water is completely dispensed in $5 \frac{1}{3}$ minutes. Show that the rate of change of the volume of water in the conical cup is given by $64\pi$ $\text{cm}^3/\text{min}$. Express the volume of water in the conical cup in terms of $h$, where $h$ is the depth of water in the conical cup. Hence find the rate of change of $h$ when $h = 6$ cm.

Accepted Answer

(i) $64\pi\text{ cm}^3\text{ min}^{-1}$ (ii) $V=\dfrac{\pi h^3}{12}\text{ cm}^3$ (iii) $\dfrac{64}{9}\text{ cm min}^{-1}$

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

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