Question

An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the slick is growing at a rate of 6 miles/hour, find the rate at which the area is increasing when the radius is 7 miles. (The area of a disc of radius r is
A = πr2.)

Answer 1

Need to find dA/dt when dr/dt = 3.5 and r = 0.5.

A(r) = π r^2

Differentiate

d/dt [A(r)] = d/dt [π r^2]
dA/dr = π 2r (dr/dt)
dA/dr = π 2(0.5) (3.5)
dA/dr = 3.5 π

Answer 2

Refer to the Mathematica calculation attached.