First slide

Rate Measure

Question

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

Moderate

A

0.4 $π$ sq. $c m / \sec$
B

0 .5 $π$ sq. $c m / \sec$ .
C

0.6 $π$ sq. $c m / \sec$
D

0.1 $π$ sq $c m / \sec$

Solution

$\frac{d r}{d t} = 0.02, r = 10$
$A = π r^{2}$
$\frac{d A}{d t} = 2 π r . \frac{d r}{d t}$
$= 2 π (10) (0.02)$ $= 2 π (0.2)$
= $0.4 π$

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