I have the following question:
given a regular tetrahedron and a sphere that goes through the middle of all sides of the regular tetrahedron, which has a bigger volume? and what is the ratio of volumes.
I know how to find the volume of a tetrahedron given his vertexes, or given his side, and also how to find the volume of a sphere given it's radius, but I couldn't solve this problem (I thought of expressing the side of the tetrahedron as x, so we know the volume of the tetrahedron, and given the fact that the sphere goes through the middle of every side, somehow find the volume of the sphere (with relation to x)).
Thanks in advance!