An offshore oil well is leaking oil onto the ocean surface forming a circular oi
ID: 3087619 • Letter: A
Question
An offshore oil well is leaking oil onto the ocean surface forming a circular oil slick .005 meter thick. If the radius of the slick is r meters, the the volume of oil spilled is V=.005(?)r^2 cubic meters. Suppose that the oil is leaking at a constant rate of 20 cubic meters per hour. Find the rate at which the radius of the oil slick is increasing at a time when the radius is 50 meters. --------- I have the actual answer, which is 40/? meters/hour but i need to know how to do it. I mostly just need the initial equation I need to differentiate...Explanation / Answer
1. We have V = .005 ? r^2...........(1) 2. Also given is dV/dt = 20..............(2) 3. We want dr/dt, so differentiate (1) with respect to t. dV/dt = .005 ? (2r) dr/dt..........(3) 4. Plug in the given condition r = 50 and (2) into (3). 20 = .005 ? (2*50) dr/dt dr/dt = 40/?