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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!

the volume of a sphere is+V+=+%284%2F3%29+pi%2Ar%5E3
if diameter of spherical balls 1.5cm, radius is r=1.5cm%2F2=0.75cm

V+=+%284%2F3%29+pi%2A%280.75cm%29%5E3
V+=+1.767145cm%5E3

a box measuring 6cm+ by 3cm by 3cm has a volume
V+=+6cm%2A3cm%2A3cm
V+=+54cm%5E3

how many balls as possible are packed in the box:
54cm%5E3%2F1.767145cm%5E3
=54%2F1.767145
=30.56
so, max is 30 balls

how much free space remains in the box:
find the volume of 30 balls and deduct from the volume of the box
V+=+30%2A1.767145cm%5E3
V+=+53.01435cm%5E3
54cm%5E3-53.01435cm%5E3
0.9857cm%5E3-> free space remains in the box

Answer by greenestamps(13200) About Me  (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.