A circular disc of radius 3 text{ cm} is bein | vedclass

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(A) Let $r$ be the radius of the circular disc and $A$ be its area.The area of the disc is given by $A = \pi r^2$.Differentiating both sides with resp

Vedclass · Accepted Answer

$0.320\pi 	ext{ cm}^2	ext{/s}$

Vedclass · Answer

(A) Let $r$ be the radius of the circular disc and $A$ be its area.The area of the disc is given by $A = \pi r^2$.Differentiating both sides with respect to time $t$,we get:$\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$.Given that the rate of increase of the radius is $\frac{dr}{dt} = 0.05 	ext{ cm/s}$.We need to find the rate of increase of the area when $r = 3.2 	ext{ cm}$.Substituting the values into the derivative formula:$\frac{dA}{dt} = 2 	imes \pi 	imes (3.2 	ext{ cm}) 	imes (0.05 	ext{ cm/s})$$\frac{dA}{dt} = 2 	imes 3.2 	imes 0.05 	imes \pi 	ext{ cm}^2	ext{/s}$$\frac{dA}{dt} = 0.320\pi 	ext{ cm}^2	ext{/s}$.Thus,the rate at which the area is increasing is $0.320\pi 	ext{ cm}^2	ext{/s}$.

$A$ circular disc of radius $3 \text{ cm}$ is being heated. Due to expansion,its radius increases at the rate of $0.05 \text{ cm/s}$. Find the rate at which its area is increasing when the radius is $3.2 \text{ cm}$.

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