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[Music]
welcome to math with mr j
[Music]
in this video i'm going to cover how to
find the surface area
of a cylinder and remember surface area
is the total
area of the outside part or layer of a
3d figure
so let's get into our example here and
on the left hand side of your screen
we have the cylinder that we're going to
find the surface area of
it has a given height of 8 inches and
our
base has a radius of 3 inches now
on the right hand side of your screen
i'll draw an arrow to it we have the
net of that cylinder so we took the 3d
figure
and unfolded it so we see all the
different parts that make up that
cylinder
as a flat figure there and this is going
to help us
visualize and see what parts that we're
going to find the area
of and then add together in order to get
the surface area
so at the top of your screen we have the
formula that we're going to use
the bottom formula here i'll underline
it this is the official formula
that we're going to use in order to find
the surface area
but the top one kind of breaks it down
and tells us
exactly what we'll be doing so the top
one
surface area equals two times the area
of the base plus the area of the
rectangle
now the one below it has the official
formulas
so pi r squared here that's the formula
for the area of a circle our top and
bottom
the bases are circles and we can
multiply
it by two if we find the area of one we
have the area of both because they're
both the exact same that's why we're
multiplying it by two so find the area
of one
multiply it by two and then we have
two pi r h so 2 pi
r that is the formula for the
circumference of a circle
so let's take a look at this rectangle
within our net so we have the height
here that's going to match our 8 inches
so that rectangle has a height of
8. now this side length
is going to be the circumference of our
base
circles there so if we took this circle
and kind of
folded it down and made it a flat line
it would
match this side of the rectangle
exactly so that's why we have
circumference within the formula for the
area
of that rectangle so we need to find the
circumference multiply
by the height and we have the area of
the rectangle
so let's plug in all the information we
have
solve and get the correct surface area
here so we will start by rewriting our
formula surface area equals
2 pi r squared
plus 2 pi
r h so now we plug in
so two pi the radius
is three squared
plus two pi radius is three of our base
again
times the height of 8
and we can start simplifying this
and work our way down to the correct
answer
so let's do 3 squared here which is
9 times 2 is 18.
so we end up with 18 pi
plus let's do 3 times 8
is 24 times 2 is
48 so we get to 48 pi
on this side so we have 18 pi
plus 48 pi so that's going to give us
18 plus 48 is 66 so we get
to 66 pi
and i'm going to use the pi button on a
calculator in order to find this final
answer
if you use the approximate or rounded
version of
pi 3.14 three and fourteen hundredths
that's very common to do
your answer may be slightly different
than mine
but it is correct you just use the
rounded version of pi
i'm using the button on the calculator
which is the more
extended version of pi so once i plug
that in
i'm going to come to the right where i
have more room i get surface area
equals 207
and i get a very long decimal so i'm
going to round this
to the nearest hundredth so i get
35 hundredths 0.35 and this is surface
area
and we're working with inches so it's
square
inches so we get a final answer of 207
and 35 hundredths square inches
so there you have it there's how you
find the surface area of a cylinder
we find the area of the base the
circular top there we multiplied it by 2
because we have two circles and we added
that to the area
of the rectangle and we end up with for
this particular example
207 and 35 hundredths square inches
i hope that helped thanks so much for
watching until next time
peace
