11cm2s−1
22cm2s−1
33cm2s−1
44cm2s−1
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 = (176−154)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}
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