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JAMB Mathematics 2021 Paper

Question : 3

Total: 40

Solution:

Concept:

The volume of a hemisphere is

V = \frac{2}{3}\pi r^{3}

. The rate of change of volume with respect to radius is the derivative

\frac{dV}{dr}

Explanation:

Differentiate the volume formula with respect to

r

\frac{dV}{dr} = \frac{d}{dr}\left(\frac{2}{3}\pi r^{3}\right) = \frac{2}{3}\pi \cdot 3r^{2} = 2\pi r^{2}

Now substitute

r = 2

into the derivative.

\frac{dV}{dr} = 2\pi (2)^{2} = 2\pi \cdot 4 = 8\pi

Answer:

The rate of change is

8\pi

, which corresponds to option A.

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