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# Find the rate of change of the volume, $$V$$ of a sphere with respect to its radius, $$r$$...

### Question

Find the rate of change of the volume, $$V$$ of a sphere with respect to its radius, $$r$$ when $$r = 1.$$

### Options

A) $$12\pi$$

B) $$4\pi$$

C) $$24\pi$$

D) $$8\pi$$

### Explanation:

Volume of sphere, $$V = \frac{4}{3} \times \pi r^3$$
Rate of change of $$V = \frac{dv}{dr}$$
Thus if, $$V = \frac{4}{3} \times \pi r^3,$$
$$\Rightarrow \frac{dv}{dr} = 4\pi^2$$
At $$r = 1,$$ Rate $$= 4 \times \pi \times 1 = 4\pi$$

## Dicussion (1)

• Volume of sphere, $$V = \frac{4}{3} \times \pi r^3$$
Rate of change of $$V = \frac{dv}{dr}$$
Thus if, $$V = \frac{4}{3} \times \pi r^3,$$
$$\Rightarrow \frac{dv}{dr} = 4\pi^2$$
At $$r = 1,$$ Rate $$= 4 \times \pi \times 1 = 4\pi$$

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