There is a box of cuboid shape. The smallest side of the box is 20 cm and largest side is 40 cm. Which of the following can be volume (in cm$$^3$$) of the box?

We know that , Volume of a cuboid is $$\left(l\times b\times h\right)\ .$$

So, if we consider given Volume's :

For 18000 :

$$40\times20\times x\ =\ 18000\ .$$

or, $$x\ =\ 22.5\ .$$

which means that this side length is lies between 20 and 40 .

So, 18000 can be the volume .

For 12000 :

$$40\times20\times x=12000\ .$$

or, $$x=15\ .$$

But given that smallest side is 20 .

So, 12000 is not possible volume .

For 36000:

$$40\times20\times x=36000\ .$$

or, $$x=45\ .$$

But given that largest side is 40.

So, 36000 is not possible volume.

For 42000 :

$$20\times40\times\ x=42000\ .$$

or, x=52.5 .

But given that largest side is 40 .

So,42000 is not possible volume .

A is correct choice.