The rate of change of the area of a circle wi | vedclass

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Question

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

Vedclass · Accepted Answer

$12 \pi 	ext{ cm}^2/	ext{cm}$

Vedclass · Answer

(B) The area of a circle $A$ with radius $r$ is given by the formula: $A = \pi r^2$ To find the rate of change of the area with respect to its radius $r$,we differentiate $A$ with respect to $r$: $\frac{dA}{dr} = \frac{d}{dr}(\pi r^2) = 2 \pi r$ Now,we evaluate this derivative at $r = 6 	ext{ cm}$: $\frac{dA}{dr} = 2 \pi (6) = 12 \pi 	ext{ cm}^2/	ext{cm}$ Thus,the rate of change of the area of the circle with respect to its radius at $r = 6 	ext{ cm}$ is $12 \pi 	ext{ cm}^2/	ext{cm}$. The correct option is $B$.

The rate of change of the area of a circle with respect to its radius $r$ at $r = 6 \text{ cm}$ is

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