Question

. A rock drops into a still lake, creating a circular ripple that expands so that the radius grows at a rate of
1.5 feet per second. At the moment when the area is 16π square feet, find the rate of change of the
following: a) the area and b) the circumference

Answer 1

when A = 16π, r=4, C = 2πr = 8π
dA = C dr, so
(a) dA/dt = 8π * 1.5 = 12π ft^2/s
(b) dC/dt = 2π dr/dt = 3π ft/s

Answer 2

Thanks oobleck