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Question
Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm ?
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Solution
Let A be the area of the circular disc. Then,
A = \[\pi r^2\]
\[\Rightarrow \frac{dA}{dr} = 2\pi r\]
Let C be the circumference of the circular disc. Then,
C = \[2\pi r\]
\[\Rightarrow \frac{dC}{dr} = 2\pi\]
\[\therefore \frac{dA}{dC} = \frac{\frac{dA}{dr}}{\frac{dC}{dr}}\]
\[ \Rightarrow \frac{dA}{dC} = \frac{2\pi r}{2\pi} = r\]
\[ \Rightarrow \left( \frac{dA}{dC} \right)_{r = 3} = 3 cm \]
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