Hint to Riddle #86: Frosty The Snowman

86. Frosty the Snowman wants to create a small snowman friend for himself. The new snowman needs a base, torso, and a head, all three of which should be spheres. The torso should be no larger than the base and the head should be no larger than the torso.

For building material, Frosty has a spherical snowball with a 6 inch radius. Since Frosty likes to keep things simple, he also wants the radius of each of the three pieces to be a positive integer. Can Frosty accomplish this?
3 spheres stacked on top of each other to make a 'snowman'
So the formula for the volume of a sphere is 4/3 π r3, lets label the base 'a', the torso 'b' and the head 'c.' So we can equate the volume of our 6 inch ball, with the volumes of the other 3.

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