The rate of change of area of a circle per second with respect to its radius at $r=\frac{100}{\pi} \

Question

The rate of change of area of a circle per second with respect to its radius at $r=\frac{100}{\pi} \mathrm{~cm}$ is

Professor PC Thomas Classes · Answer

Area $A = \pi r^2 \Rightarrow \frac{dA}{dr} = 2\pi r$. At $r=100/\pi$, rate is $200 	ext{ cm}^2/	ext{cm}$, equivalent to $0.02 	ext{ m}^2/	ext{s}$ dimensionally in context.