Let's start with the space we need for each sphere. If we approximate the value of the area to that of a cube that has the same dimensions of the diameter
[tex]V=H*W*D=0.8*0.8*0.8= 0.51 inches3
I can calculate the volume of the box as
[tex]V=H*W*D=3*4*7.5= 90 inches3
Finally I divide the volume of the box between the volume I need for each sphere Vt/Vs= 90/0.51 ≅ 177 balls
