## University Calculus: Early Transcendentals (3rd Edition)

$\frac{dA}{dt}=\pi\frac{cm^2}{min}$
Given $\frac{dr}{dt}=0.01\frac{cm}{min}$ and radius (r)=50 cm area (A)= $\pi r^2$ on differentiating both sides, we get: $\frac{dA}{dt}=2\pi r \frac{dr}{dt}$ r=50cm, so: $\frac{dA}{dt}=2\pi (50)\times 0.01$ $\frac{dA}{dt}=\pi\frac{cm^2}{min}$ Thus the final answer is:$\frac{dA}{dt}=\pi\frac{cm^2}{min}$