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Lory and here's your shmoop du jour brought to you

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by baseball's ask one of them to tell you a

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joke sometime there a riel stitch waited there All right

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one baseball has a circumference of nine point four inches

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another baseball has a volume of fourteen point one cubic

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inches Which of the following is true about the spheres

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Alright here the potential answers All right We're going to

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mumble our way through to baseball's Khun grew in similar

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all right so we've got thing one and thing two

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Thank you dr shmoop we're given a little bit of

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info about each one of them and we're being asked

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to make some determination about them based on that data

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Unfortunately the answer choices don't include anything like their besties

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forever or they both enjoy curling So it seems we're

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going to have to dig into the math for this

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one The answer choices deal with the balls being similar

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Khun grew int or neither so let's tackle similarity first

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the wrong sport But whatever since we're dealing with balls

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here know gigi's it should be a safe assumption that

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we've got perfect spheres since that's a kind of a

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requirement to be in the ball union since fears are

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regular solids ones that take metamucil anyway they would have

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to be similar to one another no matter their size

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If they're both perfectly spherical they'll always be similar by

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definition meaning that we can eliminate e right off the

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bat like you didn't see that one coming Okay now

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for khun grew inst for this part of the program

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will need to find the radius of each baseball in

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order to compare them Remember radius is from here to

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here All right Well if the radio air equal the

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balls will be congruent iii Exactly the same size and

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shape for the baseball that is if this radius equals

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that radius the falls were going to the same Got

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it Because it's perfect circle for the baseball with the

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circumference of nine point four inches circumference is this that's

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nine point four inches waken use the circumference of circles

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Formula c equals two pi r where c is the

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circumference and our is the radius and pies just plugging

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in what we know we get nine point four equals

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two pi r weakened by both sides by two pi

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Which gives us a radius of just about one point

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five inches All right well fur ball knew marot does

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here we're told the volume is fourteen point one cubic

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inches so we'll need to whip out the sphere volume

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formula for this one sphere volume four thirds pi r

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cubed got it that's formula We can set that equal

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to what we're told that the second ball has a

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volume of fourteen point one cubic inches then divide both

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sides by four thirds pi and take the cube root

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of fancy to get a radius of just about one

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point five inches and one point five Okay well doesn't

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that look familiar Looks like these two baseballs are congruent

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i'ii know scale factor is suggested by choices b c

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and d making the answer option A Hey that reminds

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us of the one about the baseball With a scale

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factor of five he was pulled off the starting roster 00:03:05.76 --> [endTime] until he could get himself back in shape Start

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