The only way to solve this problem with the information given is to assume that the two balls are made of the same material and that both balls are of uniform density.
Given that we can assume that the weight is directly proportional to the volume of each of the balls and since we know that the volume of a sphere is directly proportional to the cube of the diameter, we can say that the diameter is directly proportional to the cube root of the weight.
Substitute 6 and 32 for the diameter and the weight and then calculate the value of . Very important: At this point leave the value of in radical form, simplified and with the denominator rationalized.
Then, using your value for and using 4 for the weight, solve
for
Properly done, will be an integer.
John
My calculator said it, I believe it, that settles it
