Question

Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm ?

Answer 1

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 = \[2\pi r\]

\[\Rightarrow \frac{dC}{dr} = 2\pi\]

\[\therefore \frac{dA}{dC} = \frac{\frac{dA}{dr}}{\frac{dC}{dr}}\]
\[ \Rightarrow \frac{dA}{dC} = \frac{2\pi r}{2\pi} = r\]
\[ \Rightarrow \left( \frac{dA}{dC} \right)_{r = 3} = 3 cm \]