One cubic meter (1.00 m3) of aluminum has a mass of 2.70E+3kg, and 1.00m3 of silver has a mass of 1.05E+4kg. Find the radius of an aluminum sphere whose mass is the same as that of an silver sphere of radius 1.07cm.

Answer 1

You can figure out the mass of silver, then do all the conversions of mass to volume and back, or you can note that

density(Al)/density(Ag) = 2.57

So, volume(Al)/volume(Ag) = 2.57

But, the volume of a sphere scales as the cube of the radius, so the radius scales as the cube root of the volume.

radius(Al)/radius(Ag) = 1/∛2.57 = 1.07/1.37 = 0.78 cm