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?
(In reply to solution
right again on both counts!
At least I got n=8 right.
I had the bad luck to test my answer with the case n=1 which checked-out (a+b+c=3) even though incorrect!
Edited on November 25, 2019, 1:08 pm