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 cube and remember the surface area

is the total

area of the outside part or layer of a

3d

figure so when we're taking a look at

cubes

we can find the surface area by finding

the area of

one face and multiplying it by six

because a cube

has six faces and each face has the same

area so if we find the area of one face

we can just multiply it by six and we

get the surface area

there's also a formula over here that

does the exact same thing

as finding one area and multiplying it

by six it's just in formula form there

so surface area equals six

times one side length squared so let's

jump into our example

where we have a cube with a side length

of three feet

so we need to find the area of one face

so we can use area equals length times

width for a square

so for a cube we have that three feet

times well every side length

is the same for a cube it's made up of

square faces

so every side length is going to be 3

feet so we can do 3 times 3

to find the area of one face and three

times three

is nine so the area of let's say we did

the front face there

the area of that front face is nine

square feet

so over here to the right i

laid out a net of that cube a net is

when you

unfold a 3d figure so we can kind of

better visualize what we're doing here

so the front has an area of

9 square feet so we need to find

the surface area again the area of all

the faces

so we can think of it as all the faces

having an area of nine square feet

so if you kind of picture folding that

net

up we would just get this cube

right here um so

9 times 6 is going to give us the

surface area so we could do surface area

equals 9 times 6 and 9 times 6

gives us an answer of 54 square feet

so again we found the area of one face

the front here

and we have six

faces total so we multiply that nine by

six to give us the total surface area

now

i'm going to show you how to use the

formula two we could do surface area

equals six times the side length

squared so that s squared or three

squared in this case gives us the area

of one of the faces

it's the same as doing length times

width for a square

so we can plug in one of our side

lengths

which is three feet so six times

three squared now due to order of

operations we need to do

three squared first which is three times

three is nine

and then multiply by six so we get the

same answer

of 54 square feet if we use the formula

as well so there you have it there's how

you find the surface

area of a cube again find the area of

one face

and multiply that area by six because a

cube has

six faces and all of them with an

equivalent area i hope that helped

thanks so much for watching until next

time

peace