How do you solve this question Two spheres are cut from a certain uniform rock One has radius 4.50 cm The mass of the other is five times greater Calculate its radius?

Since

volume = 1/density x mass

and as the rock is uniform it has a constant density, the volume is directly related to the mass; meaning that since the mass of the second is 5 times as big as that of the first, the volume of the second is also 5 times as big as that of the first.

The ratio of volumes is the cube of the ratio of lengths; so the lengths are in the ratio of the cube root of the ratio of the volumes. The ratio of the volumes in this case is 1:5 giving the ratio of the lengths as 1:3√5

So the second radius is 3√5 (≈ 1.71) times as big as the first, making it 4.50 cm x 3√5 ≈ 7.69 cm.