The figure below is made up of 1 big cube and 1 small cube.The ratio of the length of the big cube to the length of the small cube is 2 : 1.What is the volume of the figure?

To find the volume of the figure, we first need to understand the relationship between the lengths of the sides of the cubes and their volumes.

The volume of a cube is given by the formula V = s^3, where s is the length of a side.

Given that the ratio of the lengths of the sides of the big cube to the small cube is 2:1, the ratio of their volumes will be the cube of this ratio. This is because when you triple the length of the sides of a cube, the volume increases by a factor of 2^3 = 8.

So, the volume of the big cube is 8 times the volume of the small cube.

The total volume of the figure is the sum of the volumes of the big cube and the small cube.

Without specific measurements for the sides of the cubes, we can't provide a numerical answer. But in terms of the side length of the small cube (let's call it s), the volume of the figure would be V = s^3 (for the small cube) + 8s^3 (for the big cube) = 9s^3.