The radius r of a circle is increasing at a rate of 3 centimeters per minute. Find the rate of change of the area when r = 38 centimeters.

Question

The radius r of a circle is increasing at a rate of 3 centimeters per minute. Find the rate of change of the area when r = 38 centimeters.

Answer?

Answer 1

r=38 cm,

r' = 3 cm/minute

A' = ?

A = pi(r^2)

A'(r) = 2pir(r')

A'(38) = 2pi(38)(3) = 228pi cm^2/minute

another approach is:

in one minute the radius will go from 38 to 41

in one minute the Area will go from pi(38^2) to pi(41)^2, from 1444pi to 1681pi, a difference of 237pi

one minute earlier radius went from 35 to 38

and the Area went from pi(35)^2 to pi(38^2), from 1225 to 1444pi, = 219pi

average of 237 and 219pi = exactly 228pi cm^2/minute