Reference no: EM131227790

Read question 2 then solve part A and B step by step

A helicopter arrives at an off-shore oil platform that has reported an oil leak due to a rupture in a pipe. From the helicopter, an observer determines that the leak is forming an oil spill in a circular pattern around the platform. She determines that the radius, r (in feet), of the spill is growing as a function of time, t (in minutes). The radius at time t minutes from the present is given by r(t)=5√(t+1) feet. The volume, V (in cubic feet), of oil in the spill is a function of the radius of the spill and is given by (r)=.2πr^2

(a) Using the concept of the composition of functions, determine the function that expresses the volume, V, of the oil spill as a function of time, t. (Indicate exactly how you are using the functions r and V to get your answer.) Note that the function you end up with, V(t), will allow you to determine the volume of oil in the spill using only the value of time, t, as an input. You should simplify your answer, but you may leave it in terms of π.

(b) Use your result from part (a) to find the time at which the volume of oil in the spill will reach a value of V=1250 cubic feet. Round your answer to one decimal place.