 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Spherplex (Posted on 2019-11-25) A sphere is reconstituted into n identical smaller spheres, keeping the total volume constant.

Let a be the ratio of the total surface area of the smaller spheres to the surface area of the original sphere.

Let b be the ratio of the radius of the original sphere to the radius of each of the smaller spheres.

Let c be the ratio of the volume of the original sphere to the volume of each of the smaller spheres.

What is the minimum integer value of a+b+c?

 No Solution Yet Submitted by Danish Ahmed Khan No Rating Comments: ( Back to comment list | You must be logged in to post comments.) soln | Comment 1 of 3

c = n = R^3/r^3

So, b=n^(1/3) and a=n^(2/3)

and the question becomes:

For what integer n is n^(2/3) + n^(1/3) + n also integer?

Dismissing the trivial case n=1, this next happens at n=8,
where a+b+c is 14

Edited on November 25, 2019, 9:32 am
 Posted by Steven Lord on 2019-11-25 09:26:06 Please log in:

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