# Thread: Cubic Function of a Cylinder

1. ## 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.

2. 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?

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

4. side of the rectangular sheet that forms the circumference, $\displaystyle C = x$

adjacent side that forms the height of the cylinder, $\displaystyle h = 25-x$

$\displaystyle x = 2\pi r$

$\displaystyle r = \frac{x}{2\pi}$

substitute in the expressions for $\displaystyle r$ and $\displaystyle h$ in terms of $\displaystyle x$ into the cylinder volume formula, then maximize.