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## Volume with unit cubes

## Video transcript

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.