CPM Homework Help : CALC Problem 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 ✎
1. Find the radius and height of the cylinder in terms of x.
2. Express the volume of the cylinder as a function of x.
3. Find the value of x that will maximize the volume and find the maximum value.

Hint (a):

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

Hint (a):

P = 2b + 2h
25 = 2x+2h
Solve for h.

Hint (b):

V = π(r²)(h). Substitute.

Hint (c):

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