Question

Let A be the area of a circle with radius r at time t.
If the radius changes at a rate of 2 in/sec, at what rate is the
circle's area changing when r = 1?

Answer 1

\[A = \pi r^{2}\]\[\frac{dA}{dt} = 2\pi r \frac{dr}{dt}\]dr/dt=2 in/s, so\[\frac{dA}{dt} = 2\pi (1) (2) = 4\pi\] 4 pi in/s