# What dimensions of the rectangle will result in a cylinder of maximum volume if you consider a rectangle of perimeter 12 inches in which it forms a cylinder by revolving this rectangle about one of its edges?

##### 1 Answer

Feb 5, 2015

A cylinder's volume,

The width of the rectangle, which forms the circumference,

graph{x+y=12 [-2.49, 25.99, -1.51, 12.74]}

The graph shows possible lengths for the sides of the rectangle if they must add up to 12 inches (

At what point along that curve is

graph{(12x-x^2)/(4pi) [-0.89, 13.35, -1.027, 6.1]}

Since

Since