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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 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