Again, a brief review of volumes of revolution and more applications of integrals.

1. Portage and Main
Calculus with the cars
at Portage and Main...

6. Oil is leaking from a tanker at the rate of gallons per
hour, where t is measured in hours. To the nearest gallon, how much oil
has leaked out of the tanker after 10 hours?

7. Suppose the density of a circular oil slick on the surface of a body of water is
given by kg/m 2.
(a) Suppose that the slick extends fromr = 0 to r = 1000 m. Determine the
mass of the oil slick to the nearest kg.

8. Suppose the density of a circular oil slick on the surface of a body of water is
given by kg/m 2.
(b) What is the smallest radius that contains 75% of the oil slick’s mass?

9. Suppose the density of cars, in cars/km for the first 30 km along Main Street
during certain hours of the day can be modeled by
where x represents the number of kilometers from the corner of Portage and
Main.
(a) Write a function that gives the number of cars from Portage and Main to a
point x km along Main Street. Do not simplify.
(b) To the nearest car, how many cars are there on this 30 km stretch of
road?