Question

A gum ball machine is in the shape of a sphere with a radius of 6 inches. A store manager wants to fill up the machine with jumbo gum balls, which have a radius of 0.6 inches. How many jumbo gumballs will fit in the machine?

Answer 1

≈ 640

Explanation:

The volume of the gumball machine is:

V = 4/3 π R³

And the volume of each gumball is:

V = 4/3 π r³

The ratio is:

(4/3 π R³) / (4/3 π r³)

(R/r)³

(6/0.6)³

1000

The gumball machine has a volume 1000 times greater than a gumball. However, in real life, solid spheres have gaps between them.

If we assume "close random packing", then the gumballs occupy about 64% of the space. So the gumball machine can hold approximately 640 gumballs.

Answer 2

The answer is 1000. Just had this question.