Question

There are three different cubes such that the first cube is 64 times the volume of the second, and the volume of the second cube is 27 times less than the volume of the third. Which among the following is the ratio of the side of the first cube to third cube?

Answer 1

4/3

Explanation:

If the ratio between the volumes of the first and the second cube is 64, the ratio between the sides is the cubic root of the ratio between the volumes, so:

`V1 / V2 = 64`

`s1 / s2 = \sqrt[3]{64} = 4`

Doing the same for the second and third cubes, we have:

`V2 / V3 = 1/27`

`s2/ s3 = \sqrt[3]{1/27} = 1/3`

So the ratio of the first cube side and the third cube side is:

`s1 / s3 = (s1/s2) * (s2/s3) = 4 * (1/3) = 4/3`