2. A cylindrical tank contains oil (use density as p in lb/ ft'). The radius of the tank is 3 feet, the length is 12 feet and oil enters and leaves the tank through an opening at the top. The tank is initially full of oil. Use the sketch below and complete each step below to find the work done in pumping all of the oil out of the opening at the top of the tank. You must use the axis provided. No calculators. (a) Find and expression for the volume of a single representative "slab" of oil that will move out of the tank. (b) Find the expression for the distance any single representative "slab" of oil must move to get out of the tank. (c) Find the expression for the force of a single representative "slab" of oil. (d) Set up (BUT DO NOT SOLVE), the Reimann sum that approximates the total work done in pumping all of the oil out of the tank.

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.