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.

Additional Topics in MathVolume formulas (word problems)
Product TypeSAT Math
SATSAT Math
SAT MathAdditional Topics in Math
Geometry and Measurement
Test PrepSAT Math

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

about thirty two pie So the answer is about ninety

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