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 4 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

Area = πr^2
d(area)/dt = 2πr dr/dt

given: dr/dt = 4
find: d(area)/dt when r = 7

d(area)/dt = 2π(7)(4) = 56π miles^2 / hour

Answer 2

Thank you!

Answer 3

Hmmm. Assuming that in precal you have not yet learned to take a derivative, consider that the area is increasing at a rate equal to the change in radius times the circumference. That is, if r changes very little, you are just adding a new, very thin circle to the area.

That of course, would be (2πr cm)*(4 cm/hr) = 56 cm^2/hr