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## Cell size

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# Surface area of a box (cuboid)

AP Bio: ENE‑1 (EU)

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## 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.

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