Answer to Question #2661 in Geometry for Faith

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

The volume of the cylinder is V = h*S = h* π d²/4.

There are three variants of placing the cylinder:
1. With the height of 2, therefore the diameter would be equal to the smallest of remained sides of the box: 7
The volume would be V = 2* π 7²/4 = 24.5π in³
2.With the height of 7 and with the diameter of 2.
The volume is V = 7* π 2²/4 = 7π in³.
3. With the height of 14 and with the diameter of 2 in.
V = 14 * π 2²/4 = 14π in³.
Thus the dimentions of the cylinder with the volume of maximum value is h = 2 in, r = 7/2 = 3.5 in.