Physics: Radius and Mass?

Question

One cubic meter (1.0m^3) of aluminum has a mass of 2700 kg, and a cubic meter of iron has a mass of 7860 kg. Find the radius of a solid aluminum sphere that has the same mass as a solid iron sphere of radius 2.01 cm. Answer in units of cm.

Answer 1

Because the masses that you give are for blocks that are 1 cubic meter in volume, they also serve as the densities for the two metals that you are comparing.

mass = density*volume

volume = (4/3)*pi*r^3

volume of iron sphere = (4/3)*3.14*0.0201^3 = 3.40*10^-5 m^3

mass of iron sphere = 7860* 3.40*10^-5 m^3 = 0.27 kg = mass of Aluminum Sphere

Volume of Al Sphere = 0.27/2700 = 9.90*10^-5 m^3

Radius = cube root (volume / (4/3) / pi) = 2.87 cm.

I did this using the MS calculator, and I'm not 100% sure on the numerical answer, but the process is what you need to do to solve the problem.  You should double check my answer.