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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 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
