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Question
A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. Find the rate at which its area is increasing when radius is 3.2 cm.
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Solution
\[\text { Let r be the radius and A be the area of the circular disc at any time t.Then },\]
\[A=\pi r^2 \]
\[\Rightarrow\frac{dA}{dt}=2\pi r\frac{dr}{dt}\]
\[\Rightarrow\frac{dA}{dt}=2\pi\times3.2\times0.05\left[ \because r = 3 . 2 \text { cm and } \frac{dr}{dt} = 0 . 05 cm/\sec \right]\]
\[\Rightarrow\frac{dA}{dt} {=0.32\pi cm}^2 /sec\]
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