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The radius of a circle increases at a rate of 0.5\(cms^{-1}\...

The radius of a circle increases at a rate of 0.5cms1. Find the rate of change in the area of the circle with radius 7cm. [π=227]

A.

11cm2s1

B.

22cm2s1

C.

33cm2s1

D.

44cm2s1

Correct answer is B

With radius = 7cm, Area=πr2=227×72

= 154cm2

The next second, radius = 7.5cm, Area=πr2=227×7.52

= 176cm2

Change in area = (176154)cm2=22cm2

The rate of increase = 22cm^{2}s^{-1}

OR

Area (A) = \pi r^{2} \implies \frac{\mathrm d A}{\mathrm d r} = 2\pi r

Given \frac{\mathrm d r}{\mathrm d t} = 0.5

\frac{\mathrm d A}{\mathrm d r} \times \frac{\mathrm d r}{\mathrm d t} = \frac{\mathrm d A}{\mathrm d t}

\frac{\mathrm d A}{\mathrm d t} = 2\pi r \times 0.5 = 2 \times \frac{22}{7} \times 7 \times 0.5

= 22cm^{2}s^{-1}