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welcome to math with mr j
[Music]
in this video i'm going to cover how to
find the surface area
of a cone and remember surface area is
the total
area of the outside or surface of a
three-dimensional shape
when it comes to cones we have two
surfaces
that we're going to find the area of and
then add those areas
together to get the total surface area
we have the area of the base
and then the lateral area the lateral
area is the area of the curved
surface the part that wraps around so to
speak
so that's our formula the area of the
base so this capital b
right here plus the lateral area
now we can make that even more specific
we'll use
pi r squared for the area of the
circular base
so pi r squared plus pi
r s pi r s is going to give us the
lateral area now the r stands for radius
within
that formula and then the s stands for
the slant height now i do want to
mention that it's common for an
l to be used to represent the slant
height
it doesn't matter which s or l they both
mean the same thing
as far as slant height for that formula
before we go through the example i want
to take a look at the net of a cone
to better understand surface area you
can think of a net
as an unfolded 3d shape it shows
all of the parts of a 3d shape so to
speak
so we have the lateral area right here
and we find that area using pi
times the radius times the slant height
and then we have the base right here
which is a circle so we use pi
times the radius squared we add those
areas
together and we have the surface area of
a cone
so let's jump into our example here
where we have a cone with a
base radius of 4 inches and then a slant
height
of 13 inches and the first thing that we
want to do
is write out our formula so surface area
equals we have pi
r squared plus
pi r s
once we have that we can plug in our
radius
and slant height so surface area
equals pi
radius of 4 inches and that is
squared plus pi
times the radius of 4
times the slant height of 13.
and now we're ready to solve so at this
point you can plug that into a
calculator
and either use the pi button or the
approximate
rounded version of pi 3.14
and whatever comes out on your
calculator will be the surface area of a
cone
now i'm going to continue simplifying or
breaking this down
until i get it in terms of pi and then i
will calculate
the surface area in decimal form so
let's go through some steps here
in order to do that and we'll start by
doing 4 squared which is going to give
us
16. 4 squared means 4 times 4
so let's put the area of the base in
terms of pi so we will have 16
times pi now i put the 16
before the pi symbol there because
typically speaking
when you have something in terms of pi a
number times
pi you put the number first
plus well
4 times 13 is going to give us
52 so in terms of pi for the
lateral area we're going to have 52
pi now we can add our
whole numbers together and combine our
pies so we have
surface area equals 68
pi and that's our answer in terms of
pi 68 pi is going to be the surface area
of that cone now let's calculate this
and see what 68 pi
equals and i'm going to use the pi
button on a calculator
so if you're using the approximate or
rounded version of pi
3.14 your answer is going to be slightly
different than mine
so 68 pi equals
213 and we are going to round the
decimal
to the nearest hundredth so 213
and 63 hundredths and this is
area so inches squared
and again i rounded that decimal to the
hundredths
so there you have it there's how you
find the surface area of a cone
find the area of the base and then the
lateral area
add those areas together and you have
the surface area
i hope that helped thanks so much for
watching
until next time peace
