Volume with unit cubes
We are asked, what is the volume of this box? And they tell us that each cube is a cubic foot. So just as a reminder, volume is a measure of how much space does something take up. And it's usually measured in cubic units. And here we're talking about cubic feet. And when they say that each cube is a cubic foot, they're saying that each of these little boxes, each of these cubes here, is exactly a 1 foot by 1 foot by 1 foot cube. We're in three dimensions right now. We're talking about three dimensions. 3D, you literally need three dimensions. You need how tall you are, how wide you are, and how deep you are. And for a cubic foot, each of those dimensions is one. So each of these are one cubic foot. The entire shape has one, two, three, four, five, six cubic feet in it. So the volume of this entire box is 6 cubic feet. And you see right here the unit says feet, and it has a superscript here of 3. This is feet to the third power. You could view this as feet times feet times feet, or cubic feet. So this is 6 cubic feet. Let's do a few more of these. What is the volume of this shape? So this one is quite interesting right over here. You have-- let's see if we can count these. So you have one, two, three, four, five, six, seven, eight unit boxes, or I guess these are cubic inches for this example. So we have 8 cubic inches. This is a lot of fun, especially when we get to rotate it. So here, each cube is a cubic foot again. So we have one, two, three cubic feet. Let's do one more of these. I like the ones that have these kind of crazy shapes that we have to rotate to be able to see all the boxes. So each of these is a cubic meter, which means that in each dimension, each of these boxes is a 1 by 1 by 1 meter. But how many boxes are there? Let's see. We have one. We have one. Let me see if I can get a view where I can look at it better. We have one, two, three, four, five, six boxes. So the total volume here is 6 cubic meters.