Question

What are the dimensions and volume of the largest cylinder that can be placed inside a box that has dimensions 14 in by 7 in by 2 in?

Answer 1

I see a box 2x7 that is 14 in long.
The cylinder can not have a diameter more than 2", thus radius is 1 the area of this cylinder end is A=pi r squared, or pi. The volume is 14 pi cu inches.
43.98 cu inches. Cylinder is 14 in long with radius of 1 inch.

Answer 2

There would be other configurations possible, for example the box could be
14x7 2 inches long, then the diameter of the cylinder could not exceed 7 inches or a radius of 3.5 in. The volume of the cylinder = pi(3.5)^2*2=76.9 cu in. The cylinder is 2 in. long with radius of 3.5 in. Volume of 76.9 cu in. Looks like this is the best answer as it is larger volume.