### Home > CALC3RD > Chapter Ch5 > Lesson 5.1.2 > Problem 5-14

5-14.

A rectangular piece of sheet metal with a perimeter of

Write equations for the radius and height of the cylinder in terms of

.Look at the diagram of the cylinder. The circumference of the base is equivalent to

.

Solve for.Express the volume of the cylinder as a function of

.. Substitute.Determine the value of

that will maximize the volume and calculate the maximum value.The volume will be at a maximum when its derivative is

.