Mathematics

Problem

A closed right circular cylinder is required to contain exactly 1,000 cm

^{3}

of fluid. Let

r

cm be the radius and

h

cm be the height of the cylinder. (a) Write an expression for the total exterior surface area

A(r,h)

of the cylinder, including both bases. (b) Use the fixed-volume condition to express

h

in terms of

r

, and write

A

as a function

A(r)

of one variable. (c) Determine the dimensions

r

and

h

that minimize the total exterior surface area. (d) Calculate the minimum surface area to the nearest whole square centimeter and interpret what this value represents in the manufacturing context.

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