Question

Let A be the area of a circle with radius r. If \[dr/dt\] =2, find \[dA/dt\] when r = 1.

I can't think of a way to set up this problem.

Answer 1

\[A= \pi r^2\]

Answer 2

\[\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt}\]

Answer 3

\[\frac{dA}{dr}= 2 \pi r \] from differentiating the first line.

Answer 4

So \[\frac{dA}{dt} = 2 \pi r \times 2 = 4 \pi r = 4\pi (1) =4\pi\]