Question

The area of a circular sun spot is growing at a rate of 1,400 km2/s. (a) How fast is the radius growing at the instant when it equals 5,000 km?

Answer 1

\[A = \pi r^2\]
\[\frac{dA}{dt} = \pi(2r) \frac{dr}{dt}\]
plug in dA/dt = 1400
r = 5000

solve for dr/dt