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Q.

The radius of a circular plate is increasing at the rate of 0.01 cm/sec. When the radius is 12 cm, the rate at which the area increases is (in square cm/sec)

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a

$60 π$

b

$24 π$

c

$1.2 π$

d

$0.24 π$

answer is D.

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Detailed Solution

$\frac{d r}{d t} = 0.01 c m / s$ , when $r = 12 c m$ , then $\frac{d A}{d t} = ?$
$A = π r^{2} \Rightarrow \frac{d A}{d t} = 2 π r \frac{d r}{d t}$
$\Rightarrow \frac{d A}{d t} = 2 π (12) \cdot (0.01) \Rightarrow \frac{24}{100} π \Rightarrow 0.24 π$

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The radius of a circular plate is increasing at the rate of 0.01 cm/sec. When the radius is 12 cm, the rate at which the area increases is (in square cm/sec)