Sphere: surface area rate from volume rate

Given the rate of change of volume of a sphere, find the rate of change of surface area at a specific radius or diameter.

1 questions · Standard +0.3

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SPS SPS FM Pure 2023 June Q6

5 marks Standard +0.3

A spherical balloon is inflated so that its volume increases at a rate of \(10\text{ cm}^3\) per second. Find the rate of increase of the balloon's surface area when its diameter is 8 cm. [For a sphere of radius \(r\), surface area \(= 4\pi r^2\) and volume \(= \frac{4}{3}\pi r^3\)]. [5]