Question 285377
what is the volume of the region inside a 6 inch cube but outside the sphere?
------------
Find the diagonal of the cube:
---
hypotenuse of a face: 6*sqrt(2)
------
diagonal = sqrt(6^2 + (6sqrt(2))^2)
diagonal = sqrt(36 + 72)
diagonal = 6sqrt(3)
---
Therefore the radius of the sphere = (1/2)diagonal = 3sqrt(3)
---------------------------------
So the volume of the sphere = (4/3)(pi)(3sqrt(3))^3
------------------------------------
The volume of the cube = 6^3 = 216
=======================================
Volume within the sphere but outside the cube 
= (4/3)pi(3sqrt(3)^3 - 216
================================
Cheers,
Stan H.