Find the dimensions of an open top circular cylinder to minimize the surface area if the volume is 27π cubic inches.

A manufacturer of canned food packages the product in cylindrical tin cans. The volume of each can is to be equal to a given value of V cubic units. Find the ratio of the height of the can to its radius to minimize its surface area.

n the mid-20th century, engineers constructed a series of canals to move irrigation water from water sources to farming communities throughout the western United States. The volume of water a canal an move is partially dependent on its cross-sectional area. Suppose a canal is trapezoidal, 35.0 ft across the top and 15.0 ft across the bottom, with a planned depth of water of 10.0 ft as shown in the gure. Find the cross-sectional area of the canal when it is full (in ft). (Use the rules for working with measurements to give your answer to the appropriate accuracy and/or precision.) 35.0 ft 10.0 ft 15.0 ft