calc

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oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per minute. The oil slick takes the form of a right circular cylinder with both its radius r and height changing h is given by V= pie times r to the second power times h)

b) a recovery device arrives on the scene and begins removing oil. The rate at which oil is removed is R(t)=400 times square root of t cubics per min, where t is the time in min since the device began working.oil continues to leak at the rate of 2000 cubic cm per min. Find t when oil slick reaches its max volume.

c) By the time the recovery device began removing oil 60000 cubic cm of oil had already leaked. write but not evauate and expression involving an integral that gives the volume of oil at the time found in part (b)

• calc -

V = pi r^2 h
dV/dt = 2000 - 400 t^.5

b) when is dV/dt = 0?
400 t^.5 = 2000
sqrt t = 5
t = 25 min

c) V at t=0 = 60,000
dV/dt = 2000 -400 t^.5
V = 60,000 + integral from t = 0 to t = 25 of (2000 - 400 t^.5) dt