Asked by Amanda
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.)
Answers
Answered by
Reiny
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
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
Answered by
Amanda
Thank you!
Answered by
Steve
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
That of course, would be (2πr cm)*(4 cm/hr) = 56 cm^2/hr
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