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Answer to Question #2661 in Geometry for Faith

Question #2661
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?
Expert's answer
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.

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