Question: The soot produced by a garbage incinerator spreads out in a circular pattern. The depth, H(r), in : millimeters, of the soot deposited each month at a distance r kilometers from the incinerator is given by H(r)=0.115e-2r.
(a) Write a definite integral giving the total volume of soot deposited within 5 kilometers of the incinerator each month.
(b) Evaluate the integral you found in part (a), giving your answer in cubic meters.