Need up to 30 seconds to load.

[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