SOLUTION: spherical balls 1.5 cm in diameter are packed in a box measuring 6 cm by 3 cm by 3 cm. if as many balls as possible are packed in the box, how much free space remains in the box?

Question 1178422: spherical balls 1.5 cm in diameter are packed in a box measuring 6 cm by 3 cm by 3 cm. if as many balls as possible are packed in the box, how much free space remains in the box?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

the volume of a sphere is
if diameter of spherical balls , radius is

a box measuring by by has a volume

how many balls as possible are packed in the box:

=
=
so, max is balls

how much free space remains in the box:
find the volume of balls and deduct from the volume of the box

-> free space remains in the box

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The response from tutor @MathLover1 is absurd -- unless the spherical balls are silly putty or some similar infinitely malleable material.

Assuming the spheres remain as spheres when packed into the box, the dimensions of the box and the diameter of the spheres make the array of balls 4 by 2 by 2, for a total of 4*2*2=16 balls.

The amount of free space in the box is then the volume of the box, minus the volume of 16 spheres of diameter 1.5 cm.

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