Main content

## AP®︎/College Biology

# Surface area of a box (cuboid)

Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw.

## Want to join the conversation?

- what is a cuboid and why use a cereal box.(28 votes)
- Palomo’s reply was confusing. A cuboid is basically a
**box**. A cereal box is a good example of a cuboid.(45 votes)

- what if all i get for length is fractions?(21 votes)
- That's
`totally`

ok! You just have to find the numbers you can multiply most easily in a specific order.(15 votes)

- does SIDE and FACE means the same things? that is surface area?(17 votes)
- the SIDE and the FACE are the same things in usual context.

One SIDE of a square is going to be equal to all the other SIDES of a square. A side is a face.(14 votes)

- why do they make it so hard 😢(14 votes)
- It means that you are learning something which takes time to tackle. It doesn't happen in a day or even in a few.(14 votes)

- So, if I was to calculate the area of cuboid
**and**the volume, would it be close in value? 600 is the volume of that box and 580 is the area, but are these two values always proportional?(11 votes)- No, they have no relation. The area of the cuboid isn't proportional to the volume. If the proportions of the sides are given, yes, but as a general rule, they aren't.(5 votes)

- how do you get the surface area?(6 votes)
- The surface area of the rectangular prism(or cube)

is S=Ph+2B

S=Surface Area

P=perimeter of the base(you can choose any two parallel sides for the base)

h=height between 2 bases

2B=area of bases times 2(14 votes)

- Is there a more simpler formula to find the surface area of a cubiod? I don't understand the meaning of SA=2lw+2lh+2hw, my teacher told me a different formula to figure out the surface area of a cuboid but I forgot it.(5 votes)
- Not unless it is a perfect cube (I.e. all sides have same length l=h=w). If, and only if, that is the case, then that formula you have simplifies to SA = 6x^2.(8 votes)

- Were did the 60 come from? What do you do first when you got only 2 numbers?(4 votes)
- OK, lets go through this piece by piece. There are 6 sides to the box with the following dimensions:

Front is 20 cm by 10 cm

Back is 20 cm by 10 cm

Left is 20 cm by 3 cm

Right is 20 cm by 3 cm

Top is 10 cm by 3 cm

Bottom is 10 cm by 3 cm

Their areas are:

Front: 20 * 10 = 200 cm^2

Back: 20 * 10 = 200 cm^2

Left: 20 * 3 = 60 cm^2

Right: 20 * 3 = 60 cm^2

Top: 10 * 3 = 30 cm^2

Bottom: 10 * 3 = 30 cm^2

So the area is 200 + 200 + 60 + 60 + 30 + 30 = 580(9 votes)

- what happens if you have 60 cm2 and 20 cm2 on the same side of a square?(8 votes)
- how do you find the surface area of a triangular prism?(5 votes)

## Video transcript

- [Voiceover] Let's see if
we can figure out the surface area of this cereal box. And there's a couple of ways to tackle it. The first way is, well let's
figure out the surface area of the sides that we can
see, and then think about what the surface area of the
sides that we can't see are and how they might relate, and
then add them all together. So let's do that. So the front of the box
is 20 centimeters tall and 10 centimeters wide. It's a rectangle, so to figure
out its area we can just multiply 20 centimeters
times 10 centimeters, and that's going to
give us 200 centimeters. 200 centimeters, or 200 square
centimeters, I should say. 200 square centimeters,
that's the area of the front. And let me write it right
over here as well, 200. Now we also know there's
another side that has the exact same area as the
front of the box, and that's the back of the box. And so let's write another
200 square centimeters for the back of the box. Now let's figure out the
area of the top of the box. The top of the box, we see the
box is three centimeters deep so this right over here
is three centimeters. It's three centimeters deep
and it's 10 centimeters wide. We see the box is 10 centimeters wide. So the top of the box is
gonna be three centimeters times 10 centimeters, which
is 30 square centimeters of area. So that's the top of the
box, 30 square centimeters. Well, the bottom of the
box is gonna have the exact same area, we just can't
see it right now, so that's gonna be another 30. Then we have two more sides,
cuz this box has six sides, We have this side panel
that is 20 centimeters tall, we see that the height of
the box is 20 centimeters and three centimeters deep. So three times 20, let me
write that a little bit neater. Three times 20, that's 20 centimeters right there. Three centimeters times 20 centimeters is going to give us 60 square centimeters. Now that's this side
panel, but there's another side panel that has the
exact same area that's on the other side of the box, so it's 60 centimeters squared for this side, and then another 60 for
the corresponding side opposite to it that we can't see. And now we can just add
up all of these together. And so we get zero, this is going to be carry the one, or regroup
the one, it's a 100, and then we have 500. So we get 580 square
centimeters is the surface area of this box.