Question

Hey guys, I'm really stuck with this problem. A dozen golf balls fit inside a box in the shape of a rectangular prism. The golf balls are packed tightly together and they touch the top, bottom and sides of the box. What percentage of the volume within the box is air? Please show work.

Answer 1

ok so one way of doingit is
split the box into 12 cubes around each golf ball
nnow find the wasted space that each golf ball wastes around itself since the ratio of the total percent must be the same as the total

so lets say the height of the cubes=2 so therefor volume of  each cube=2^3=8

now find the volume of each apere
volume=4/3pir^3
the height=diameter
diameter/2=radius
2/2=1=radius
volumeofsphere=4/3pi1^3
vs=4/3pi1
vs=4/3pi
aprox pi to 3.14
vs=12.56/3
vs=4.18666

so now we have
total space=8
area of ball=4.186666
percent lost=total-areauseed=8-4.18666=3.81333333
so percent lost=lost/total=3.81333/8=0.397/1
percent means parts out of 100
0.397/1 times 100/100=39.7/100=39.7%


so the answer is 39.7% wasted space (aprox 40%)