ShmoopTube

00:00

Thank you We sneak And here's your shmoop du jour

00:05

Brought to you by candy We swore we were gonna

00:08

be good and not by any of the movie theater

00:10

but we're willing to make one small concession Check this

00:14

figure out boxes Approximately seventy five percent full by volume

00:19

of spherical candies each with a diameter of zero point

00:23

five inches If the box contains one hundred thirty seven

00:27

pieces of candy what is the value of in And

00:30

here The potential answers Apparently this box of candy comes

00:36

complete with measurements variables and volume formulas it's almost enough

00:40

to take the fun right out of slowly destroying your

00:43

teeth Okay so what's the question asking we've got this

00:47

box full of candy and we're told that seventy five

00:49

percent full like someone couldn't wait for the movie to

00:52

start We're also told that the spherical candies contained therein

00:56

each have a diameter of coming five inches though they're

00:59

about this big were given the width and height of

01:02

the candy box and we know there are one hundred

01:05

thirty seven pieces of candy inside Well our job is

01:08

to find the measurement of that last side only to

01:11

start by figuring out how much space is taken up

01:14

by one of the candies For that we'll need our

01:17

trusty volume of a sphere formula which he recalled is

01:21

four thirds pi times the radius do well if the

01:25

diameter is point five inches than the radius must be

01:28

half that or point two five inches and we've got

01:31

everything we need to calculate the volume Plugging all this

01:33

business into our calculator we get roughly point o six

01:37

five four four cubic Inches That doesn't sound very big

01:41

One more couldn't hurt Now we know there are one

01:44

hundred thirty seven pieces of candy in the box so

01:46

we could multiply our result by one hundred thirty seven

01:48

to get the total volume of space being taken up

01:51

by our little chocolatey friends Point o six five four

01:54

four times one thirty seven equals eight point nine six

01:58

six six cubic inches Great So we've got the volume

02:01

of the box right Oh if only life were that

02:04

simple remember the candies air only taking up seventy five

02:07

percent of the box So our eight point nine six

02:10

six six cubic inches represents three fourths of the box

02:13

total volume though if eight point nine six six six

02:16

cubic inches is seventy five percent of the volume we

02:19

can multiply by four third's to get the volume of

02:22

the whole kit and caboodle That will give us eleven

02:25

point nine five five five cubic inches Hell didn't sound

02:28

like all that much Now we're trying to find the

02:31

volume of the box using our formula for a rectangular

02:34

prism It's just length times with times height while we

02:37

have two of those Three with the other roving in

02:40

the volume of the box is also six times four

02:44

times end or twenty for end Next we consent twenty

02:47

for an equal to eleven point nine five five five

02:50

since we know that both represent the volume of the

02:52

box and divide both sides by twenty four To get

02:54

n equals point Four nine eight or almost exactly point

02:58

five inches Cute that it be Option c which comes

03:01

very close to hitting the nail directly on the head

03:03

Oof Those tiny half inch candie's you add up quickly 00:03:07.78 --> [endTime] as can one's dental bills

Full Transcript