Posted by JOY on .
4 balls each with a radius 1 inch fit snuggly into a 2x2x8 inch box. Is the total volume left over inside the box greater than or less than the volume of a fifth ball? Justify answer.
I got as far as figuring the volume of box is 32 cubic inches
I'm not sure about the balls?

Geometry 
MathMate,
Volume of 1 ball, of radius r
V=4πr^3/3
=4π1^3/3
=4π/3
Interstitial volume (empty space)
= 32 in.³  4V
You will find that the volume left over is just slightly less than half the volume of the box.