Q.

The radius of a circular plate is increasing at the rate of 0.02 cm/sec. when the radius is 10cm. Then the rate at which the area increases is

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a

0.4π  sq.cm/sec

b

0 .5π  sq.cm/sec .

c

0.6π  sq.cm/sec

d

0.1π  sqcm/sec

answer is A.

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Detailed Solution

drdt=0.02, r=10 A=πr2  dAdt=2πr.drdt=2π(10)(0.02)=2π(0.2)  = 0.4π
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The radius of a circular plate is increasing at the rate of 0.02 cm/sec. when the radius is 10cm. Then the rate at which the area increases is