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 3.5 miles/hour, find the rate at which the area is increasing when the radius is 1.5 miles. (The area of a disk of radius r is A = πr2. Enter your answer in terms of π.)
______?=mi^2/h

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 3.5 miles/hour, find the rate at which the area is increasing when the radius is 1.5 miles. (The area of a disk of radius r is A = πr2. Enter your answer in terms of π.)
______?=mi^2/h

anonymous · Answer

This is a related rate problem. Identify what the question is asking you to find, and put down any relevant formulas as well as any other given derivatives/rates

cwrw238 · Answer

dr/dt = 3.5
dA/dt = d(pir^2) / dt

anonymous · Answer

its asking us to find the rate the area is increasing at given distance being the radius at 1.5 how ever i would have no idea how to solve

cwrw238 · Answer

at r = 1.5  dA /dr = 2 pi r = 2*1.5 pi = 3pi  

dA/dt =  dA/dr * dr/dt =  3pi * 3.5 =  10.5 pi

cwrw238 · Answer

do you follow that ok?

anonymous · Answer

yes then what do i do after tht?

cwrw238 · Answer

thats the answer 10.5 mi^2 / h

cwrw238 · Answer

sorry 10.5 pi m^2/h

anonymous · Answer

it is thank you very much for explaining how

cwrw238 · Answer

yw