Use the method of cylindrical shells to find the volume generated by rotating the region bounded by y = 3 + 2x – x² and X +y = 3 about the y-axis. Volume =

Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the lines x = 9 and y = 5 is revolved about the a) x-axis b) y-axis

Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a lateral area. b total area. c volume.

A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2