# SAT Math: Applying the Volumes of Cubes and Spheres to Packing Ping-Pong Balls

Timothy is moving and wants to pack his ping pong balls into the box shown above. Each ping pong ball has a diameter of 2 inches. If he packs this box with the maximum number of ping pong balls possible, how much empty space in cubic inches would the box have? Round to two decimal places.

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### Transcript

02:13

out how much space there is in the box It's

02:16

occupied by the ping pong ball so it's a volume

02:19

question We've got the volume of a sphere Remember that

02:21

formula four thirds pi r cubed Well the diameter the

02:24

balls two inches So the radius is half of that

02:26

which is one inch and the amount of empty space

02:28

in the box The volume ball ping pong balls subtracted

02:30

from the total volume of the box So it's pretty

02:32

simple right So let's see that's going to give us

02:35

this equation here four times eight times six minus twenty

02:38

four times this quantity It's a building with box and

02:40

that'll just simplify too Well See the volume of the

02:44

box was for a sex that's one ninety two cubic

02:47

inches and that we're going to subtract the volume of

02:49

the ping pong balls that they take up which is

02:51

02:54

one point four seven That is there would be approximately

02:57

ninety one point four seven cubic inches of empty space

02:59

left in the box Maybe timothy can fill that space

03:03

with his toy story tears Anything All right we're done