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?

Accepted Solution

Answer:≈ 640Step-by-step explanation:The volume of the gumball machine is:V = 4/3 π R³And the volume of each gumball is:V = 4/3 π r³The ratio is:(4/3 π R³) / (4/3 π r³)(R/r)³(6/0.6)³1000The 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.