The radius of a circular disc is increasing at a constant rate of 0.003cm/s. Find the rate at which the area is increasing when the radius is 20cm.

The rate at which the area is increasing, dA/dt, can be written with terms we know or can find out easily: dA/dt=dA/dr x dr/dt.Area of a disc, A = (pi)r^2dA/dr=2(pi)rRate of change of radius, dr/dt=0.003cm/sTherefore, dA/dt=2(pi)r x 0.003= 2(pi) x 20 x 0.003=0.12(pi)= 0.377cm^2/s