Question

1m3 of aluminum has a mass of 4x106 gram and 1m3 of iron has a mass of 10x106 gram. Find the radius of a solid aluminum sphere in meter that will balance a solid iron sphere of radius 4cm on an equal arm balance.

Answer 1

Their mass must be the same:

$$\rho_a·\frac43\pi r_a^3=\rho_i·\frac43\pi r_i^3,\\\space\\ r_a=r_i\sqrt[3]{\rho_i/\rho_a}=5.43\text{ cm}.$$