Question

Given a sphere perfectly inscribed inside of a regular square pyramid.
Find the ratio of the volume of sphere to volume of pyramid.

good luck (exact answers only)

Answer 1

drawing of base and triangular face

Answer 2

pi (3sqrt(3)-5) : 2 ??

Answer 3

congrats!
not in same form as my solution, but numerically the same
\[ratio = \frac{\sqrt{2}}{16}(\sqrt{6}-\sqrt{2})^{3} \pi : 1\]

Answer 4

yesss !! :)