Postal regulations specify that a package sent by a certain shipping method may have a combined length and girth of no more than 96 in. Find the dimensions of a cylindrical package with the greatest volume that may be sent by this shipping method. Hint: The length plus the girth is 2πr + l. (Round your answers to three decimal places.)

A piece of hardware is constructed by drilling a cylindrical hole through a right prism with a square base that measures 20 mm on each side. The hole is 35 mm long, as shown in the diagram. Determine the volume of the remaining material once the hole has been drilled. Round your answer if necessary to the nearest cubic millimeter. Use 3.14 for π ..

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 14 in. by 9 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume. (Round to the nearest 100th.)

Given two sheets of paper: (A) 8-1/2" x 11" and (B) 11" x 8-1/2" To answer the following questions, roll each sheet of paper into the shape of a cylinder. 1. Which one has the greater volume once rolled into a cylinder, A or B? 2. To the nearest hundredth, what is the volume of the cylinder created by paper A? 3. To the nearest tenth, what is the lateral area of the cylinder created by paper B?