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welcome to math with mr j

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in this video i'm going to cover how to

find the volume of a cylinder

and remember volume is the amount of

space a three-dimensional object

takes up so let's get into our example

here

where we have a cylinder with a given

height of 8 inches

and our base has a given radius of 3

inches

so that's the information we need in

order to

calculate volume of a cylinder now we

have

two formulas at the top of our screen

here

they look different but they mean the

exact same thing so the top one says

volume

equals a capital b times h

so that capital b means the area of the

base

times h which is height now the formula

below that

says volume equals pi r squared

so pi times radius squared times height

now pi r squared that's the formula

for the area of a circle so

in the case of this cylinder our base is

a circle so the

area of the base that capital b

expanded out to the formula we're going

to use pi r squared

would give us that formula that's below

so they mean the same thing they just

look a little different

so now we plug in our givens that height

and radius of the base

into our formula in order to calculate

the

volume of this cylinder so we will come

to the side

we'll rewrite our formula pi

times radius squared times height

then we will plug in so pi

times the radius of our base which is

three inches

squared times the height of eight

inches so time to simplify and work our

way down to

the final answer so we will do one step

at a time here so

three squared would be first which means

three times three

and that gives us nine times the height

of

eight so next step we could do 9 times

8 which is 72

and we multiply that by pi so i put the

72 before the pi because typically when

you multiply something by pi you put the

number first and multiplication is

commutative

so you can switch the order of things

and still get the same answer for

example 3 times 2 is 6

and 2 times 3 is 6. it doesn't matter

the order

so 72 times pi as far as that goes i'm

going to use the pi button

on my calculator when i punch this in if

you are using

the approximate or rounded pi 3.14 which

is common to do

you may get a slightly different answer

than me but you are still correct

you just use the rounded version of pi

so once i punch that

in i get a pretty long decimal there so

i'm going to

round it to the hundredths place again

i'm rounding my answer to the hundredths

place

and i get 226 and

19 hundredths and this is volume so we

use

cubic inches or i'm sorry

cubic whatever the unit of measure is

and in this case

we were working with inches so cubic

inches so volume

equals 226 and 19 hundredths

cubic inches so there's how you find the

volume of a cylinder

we found the area of the base and

multiplied it by the height

now our base was a circle so we use

pi r squared in order to calculate the

area of our base

and multiplied it by the height i hope

that helped

thanks so much for watching until next

time peace