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.
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`