S h r Figure 1: The right cone. Let us find the volume of a right cone. The base of the cone is a circle with radius r, and the height of the cone is h. (a) If we look at a thin slice of the cone, that is a horizontal cross section with a distance r away from the base, what is the area of this cross section in terms of r, h? ( 3 Points.) (b) Use the definite integral to find the volume of the cone as a function of r, h. ( 6 Points.) (c) Let us now make a small change. Let the vertical line in the figure with length h to have an angle 0 with the base. For the right cone, 0 = 7/2. If we keep h, r fixed, derive the formula for the volume of the cone for 0