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Geometry and Measurement Videos 87 videos

SAT Math 1.1 Geometry and Measurement
719 Views

SAT Math 1.1 Geometry and Measurement. What is the circumference of the circle?

SAT Math 1.2 Geometry and Measurement
246 Views

SAT Math: Geometry and Measurement Drill 1, Problem 2. If A = (0, 4), B = (-3, 2), and C = (1, 0), which point is in the interior of angle ABC?

SAT Math 1.3 Geometry and Measurement
231 Views

SAT Math 1.3 Geometry and Measurement. Find the length of CE.

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SAT Math: Applying the Volumes of Cubes and Spheres to Packing Ping-Pong Balls 13 Views


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Description:

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.


Transcript

00:00

Yeah News twenty four and eight packs time three twenty

02:02

four twenty four is the number Timothy compact 204 ping

02:05

pong ball so he can prep for a really intense

02:08

game of ping pong War on the problem Asked how

02:10

much empty space there is left so we're gonna find

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

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