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 d^{2}/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 7^{2}/4 = 24.5π in^{3}

2.With the height of 7 and with the diameter of 2.

The volume is V = 7* π 2^{2}/4 = 7π in^{3}.

3. With the height of 14 and with the diameter of 2 in.

V = 14 * π 2^{2}/4 = 14π in^{3}.

Thus the dimentions of the cylinder with the volume of maximum value is h = 2 in, r = 7/2 = 3.5 in.

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 7

2.With the height of 7 and with the diameter of 2.

The volume is V = 7* π 2

3. With the height of 14 and with the diameter of 2 in.

V = 14 * π 2

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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