If the rate of increase in area is 1.5cm/s, how would I go about finding the rate of change of radius when the area is 30cm^2?

Question

Ink is dropped on a blotting paper forming a circular stain which increases in area at a a rate of 1.5cm/s. Fin the rate of change of the radius when the area is 30cm^2.

Answer 1

A = pi r² ... Equation #1

dA/dt = 2 pi r dr/dt ... #2

when A = 30 cm² = pi r², r = √(30/pi) = 3.0902, approximately 

 

Now solve equation # 2 for dr/dt, using the above value of r and the stated value of dA/dt at that instant (i.e. 1.5)

 

This is a related rates problem.