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Question
Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm
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Solution
Let A be area of the circle. Then,
A = \[\pi r^2\]
\[\Rightarrow \frac{dA}{dr} = 2\pi r\]
Hence, the rate of change of the area of the circle is
\[2\pi r\]
When r = 5 cm,
\[\left( \frac{dA}{dr} \right)_{r = 5} = 2\pi\left( 5 \right)\]
\[ = 10\pi {cm}^2 /cm\]
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