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(C) Let $r$ be the radius of the circular wave and $A$ be the area of the circular region.Given that the rate of change of the radius is $\frac{dr}{dt

Vedclass · Accepted Answer

$132 	ext{ cm}^2/	ext{sec}$

Vedclass · Answer

(C) Let $r$ be the radius of the circular wave and $A$ be the area of the circular region.Given that the rate of change of the radius is $\frac{dr}{dt} = 2.1 	ext{ cm/sec}$.The area of the circle is given by $A = \pi r^2$.Differentiating both sides with respect to $t$,we get $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$.Given $r = 10 	ext{ cm}$ and $\frac{dr}{dt} = 2.1 	ext{ cm/sec}$.Substituting these values,$\frac{dA}{dt} = 2 	imes \frac{22}{7} 	imes 10 	imes 2.1$.$\frac{dA}{dt} = 2 	imes \frac{22}{7} 	imes 10 	imes \frac{21}{10}$.$\frac{dA}{dt} = 2 	imes 22 	imes 3 = 132 	ext{ cm}^2/	ext{sec}$.

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