Find the rate of change of the area of a circ | vedclass

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(B) The area $A$ of a circle with radius $r$ is given by $A = \pi r^2$.To find the rate of change of the area with respect to the radius,we differenti

Vedclass · Accepted Answer

$10 \pi 	ext{ cm}^2/	ext{cm}$

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(B) The area $A$ of a circle with radius $r$ is given by $A = \pi r^2$.To find the rate of change of the area with respect to the radius,we differentiate $A$ with respect to $r$:$\frac{dA}{dr} = \frac{d}{dr}(\pi r^2) = 2\pi r$.Given that $r = 5 	ext{ cm}$,we substitute this value into the derivative:$\frac{dA}{dr} = 2 	imes \pi 	imes 5 = 10\pi$.Therefore,the rate of change of the area of the circle with respect to its radius when $r = 5 	ext{ cm}$ is $10\pi 	ext{ cm}^2/	ext{cm}$.

Find the rate of change of the area of a circle with respect to its radius $r$ when $r=5 \text{ cm}$.

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