### Home > CALC > Chapter 5 > Lesson 5.1.2 > Problem 5-14

5-14.

A rectangular piece of sheet metal with a perimeter of 50 cm is rolled into a cylinder with two open ends. Homework Help ✎ Find the radius and height of the cylinder in terms of

*x*.Express the volume of the cylinder as a function of

*x*.Find the value of

*x*that will maximize the volume and find the maximum value.

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

*P* = 2*b* + 2*h*

25 = 2*x*+2*h*

Solve for *h*.

*V* = *π*(*r*²)(*h*). Substitute.

The volume will be at a maximum when its derivative is 0.