The total surface area of a sphere is increasing at the rate of $24\pi$ cm$^2$/s at the instant

Question

The total surface area of a sphere is increasing at the rate of $24\pi$ cm$^2$/s at the instant when its radius is $2$ cm. Find the rate of increase of the volume of the sphere at the same instant. Leave your answers in terms of $\pi$.

Accepted Answer

$24\pi\text{ cm}^3\text{/s}$

Differentiation

Differentiation

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