# If the maximum volume of a cube or cylinder is 2000 cubic cm what can be the maximum height, width and length of the cube or cylinder.

justaguide | College Teacher | (Level 2) Distinguished Educator

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In a cube the height, width and length are equal. If all the three are equal to N, the volume of the cube is N^3. Here N^3 can take a maximum value of 2000 cubic cm.

N^3 `<=` 2000

`=> N <= 2000^(1/3)`

`=> N <= 12.599`

The maximum dimensions of the cube can be approximately 12.599 cm.

For a cylinder, the volume is dependent on the length and the radius. The volume of the cylinder is given by pi*r^2*h. Here pi*r^2*h can take a maximum value of 2000 but there is no restriction on r and h. If r is made very small, or the cylinder is very thin, the length can be very long. Similarly if the radius is very large, the cylinder has a very short length.

The only constraints for the radius and the length is that `pi*r^2*h <= 2000` .

The maximum dimensions of the cube can be approximately 12.599 cm. And for the cylinder `pi*r^2*h <= 2000`