Thread: Cubic Function of a Cylinder

A rectangular piece of sheet metal with perimeter 50cm is rolled into a cylinder with open ends.

a) Express the volume of the cylinder as a function of x. Then give the domain of the function.
b) Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.

Originally Posted by fizz

A rectangular piece of sheet metal with perimeter 50cm is rolled into a cylinder with open ends.

a) Express the volume of the cylinder as a function of x. Then give the domain of the function.
b) Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.

what is x supposed to represent?

The circumference of the cylinder. Sorry, I forgot to include that.

side of the rectangular sheet that forms the circumference,

adjacent side that forms the height of the cylinder,






substitute in the expressions for and in terms of into the cylinder volume formula, then maximize.