A circular metal plate is heated so that its radius increases at a rate of 0.1 mm per minute. Then the rate at which the plate’s area is increasing when the radius is 50 cm, is

A circular metal plate is heated so that its radius increases at a rate of 0.1 mm per minute. Then the rate at which the plate's area is increasing when the radius is 50 cm, is

A
$10 π mm / minute$
B
$100 π mm / minute$
C
$π mm / minute$
D
$- π mm / minute$

Solution:

Let at any moment $' t'$ the radius of the plate be and its area be A. Then,

$A = π r^{2} \Rightarrow \frac{d A}{d t} = 2 π r \frac{d r}{d t}$

when $r = 50 cm = 500 mm, \frac{d r}{d t} = 0.1 = \frac{1}{10}$

$\frac{d A}{d t} = 2 π \times 500 \times \frac{1}{10} = 100 π mm / minute$

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