Question

a sphere fits snugly inside a 6-in. cube as shown. what is the volume of the region inside the cube but outside the sphere

Answer 1

assuming that means the diameter is 6in

so then

vsphere=(4/3)pir^3
r=d/2
d=6
6/2=3=r

vcube-vsphere=space
vcube=side^3=6^3=216
vsphere=(4/3)pi3^3=36pi=113.093755

space=216-113.083755=102.9026644707 cubic inches of empty space