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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
![What is Volume of a Cylinder? - [8-8-7]](https://i.ytimg.com/vi/_NXgTp8annM/mqdefault.jpg)
