Question

the radius of a circular puddle is growing at a rate of 20 cm/s. How fast is the area growing at the instant when it equals 25 cm^2? (use the area formula to determine the radius at that instant)

Answer 1

\[
A=\pi r^2\\
\frac{dA}{dt} = 2\pi r\frac{dr}{dt}
\]

the radius of a circular puddle is growing at a rate of 20 cm/s\[
\frac{dr}{dt} = 20
\]

the area growing at the instant when it equals 25 cm^2?\[
\pi r^2 = 25
\]

Answer 2

^ yep, now just find r (from that last equation) and put it into dA/dt.