Asked by andy
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.
Answers
Answered by
Steve
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
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
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