About this video
The video finds the surface area of a cereal box 20 cm tall, 10 cm wide and 3 cm deep. It works out the front (200), top (30) and side (60) in square centimetres, notes that each has a matching face on the opposite side, and adds all six faces to get 580 square centimetres.
You'll be able to
- find the area of each face of a box.
- use matching opposite faces to find areas I can't see.
- add the six face areas to find the surface area of a box.
Key words
- surface area
- The total area of all the outside faces of a 3D shape.
- square centimetres
- Units of area, written cm^2.
- face
- A flat side of a 3D shape; a box has six.
- depth
- How far the box goes from front to back, here 3 cm.
Transcript
- [Instructor] 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 lemme write it 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 is, we see it's three. The box is three centimeters deep. So this right over here is three centimeters. Three, it's three centimeters deep and it's 10 centimeters wide. We see that 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. And then we have two more sides 'cause 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, three times 20, 3 times.
Let me write that a little bit neater. Three times 20, that's 20 centimeters right there. Three centimeters times 20 centimeters is gonna give us 60 square centimeters, 60 square centimeters. Now that's this side panel, but there's another side panel that has the exact same air that's on the other side of the box.
So it's 60 centimeters squared or squared centimeters 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. Let's see, this is going to be, let's see, 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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