For each volume problem, draw a picture of the solid. Also draw a thin cross-section or a cylindrical shell. Then show a sequence of logical steps involving an integral to compute the volume. 4. Consider the region bounded by y = x%, y = 1 x?, and the y-axis for x = 0. Find the volume of the solid formed when this region is revolved about the y-axis using a) the disk method. b) the shell method. 5. A cylindrical hole of radius r is drilled downward through the center of a sphere with radius R. Find the volume of the solid that remains using a) the washer method. b) the shell method. 6. Aregular pyramid has a square base of side [ and its apex located h units above the center of its base. Use an integral to derive the volume formula in terms of [ and h. + SIMPLE JREITION X '2 Y-12 y-X'2 SOLIDS OF REVILION - X" SOMDLES Y 3 - X Z 3'2 (27) 3 02 CYINNUTARY SHELLLION