Suppose the circumference of a circle is increasing at a rate of 3 cm/s. Find the rate at which the area of the circle is changing when the area is 64pi square centimeters. nEEd ALot of HELP on this one. !! PLZ.

Question

Jayden--CUHS

Answer 1

When the area of the circle is 64 pi cm^2, the radius is 8 cm. OK so far?

The rate of change of the circumference is 2*pi*dr/dt. Since that equals 3,
dr/dt = 3/(2 pi) cm/s

The rate of change of area is
d(pi*r2)/dt = 2*pi*r* dr/dt
= 2*pi*8*[3/(2 pi)]= 24 cm^2/s

Answer 2

Thanks! :)