The length, the breadth and the height of a cuboid are doubled, the ratio between the volumes of the new cuboid and the original cuboid is :

1. 4 : 1

2. 1 : 4

3. 8 : 1

4. 1 : 8

Let l be the length, b be the breadth and h be the height of the original cuboid.

It is given that the length, breadth and height are doubled.

As we know, the volume of cuboid = length x breadth x height

The Ratio of the volume of the new cuboid to the original cuboid is:

$= \dfrac{\text{Volume of new cuboid}}{\text{Volume of old cuboid}}\\[1em] = \dfrac{2l \times 2b \times 2h}{l \times b \times h}\\[1em] = \dfrac{8lbh}{lbh}\\[1em] = \dfrac{8\cancel{lbh}}{\cancel{lbh}}\\[1em] = \dfrac{8}{1}$

Hence, option 3 is the correct option.