The volumes of two cubes are in the ratio of 8:27. If the volume of the larger cube is 513 cm
3
more than that of the smaller cube, find the length of each side of the smaller cube.

Let the volumes of the smaller and larger cubes be 8x and 27x respectively.
According to the problem:

27x−8x=513
19x=513
x=
19
513
​
=27
Thus, the volume of the smaller cube (V
1
​
) is:

V
1
​
=8x=8×27=216 cm
3

Let a be the side length of the smaller cube.

a
3
=216⟹a=
3

216

​
=6 cm