Express the volume $\"\"$ of the cylinder as a function of $\"\"$ .

Formula for the volume of the cylinder is $\"\"$ .

Observe the figure:

There are two similar triangles,

One triangle has the legs $\"\"$ and $\"\"$ .

The small right triangle with the legs $\"\"$ and $\"\"$ .

Set up the proportion:

$\"\"$

Solve for $\"\"$ .

$\"\"$

Substitute the value of $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .