Determine the most efficient calculus method needed to solve each part; include a sketch for each part. (0.2) (8,2) R1 R2 R3 (0,0) x=4y (8,0) 4. Use the figure (above) to answer parts (a) through (c) below. Find the volume obtained when the specified region is rotated about the given line. (a) Rotate R, about the y-axis.

The radius length of the base of a right circular cylinder is 6 in. The height of the cylinder is 10 in. Find the exact a Lateral area b total area c volume.

For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b volumes.

Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.

A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can, and let h denote the height, both in inches. a. Express the total surface area S of the can, using x and h. Note: The total surface area is the area of the top plus the area of the bottom plus the area of the cylinder. b. Using the fact that the total area is 40 square inches, express h in terms of x. c. Express the volume V of the can in terms of x.

Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. The frustum of a right circular cone has a larger base area of 40.0 square centimeters and a smaller base area of 19.0 square centimeters. The height is 22.0 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.

Find the exact volume of the solid that results when the rectangular region with vertices at 0, 0, 6, 0, 6, 4 and 0, 4 is revolved about the a x-axis b y-axis