A sphere with radius $r$ cm, has a surface area $A$ cm$^2$ and volume $V$ cm$^3$. Write do

Question

A sphere with radius $r$ cm, has a surface area $A$ cm$^2$ and volume $V$ cm$^3$. Write down an expression for $\dfrac{\mathrm{d}A}{\mathrm{d}r}$ and $\dfrac{\mathrm{d}V}{\mathrm{d}r}$. Given that the area is increasing at a rate of $2$ cm$^2$/s, find the rate of change of $r$ when radius is $3$ cm. Hence, find the rate of change of $V$ at this instant.

Accepted Answer

(a) $\frac{\mathrm dA}{\mathrm dr}=8\pi r,\ \frac{\mathrm dV}{\mathrm dr}=4\pi r^2$ (b) $\frac{1}{12\pi}\text{ cm s}^{-1}$ (c) $3\text{ cm}^3\text{ s}^{-1}$

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

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