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## Grade 7 (Virginia)

### Course: Grade 7 (Virginia) > Unit 7

Lesson 3: Volume- Volume with fractional cubes
- Volume with cubes of fractional side lengths
- Volume of a rectangular prism: fractional dimensions
- Volume by multiplying area of base times height
- Volume with fractions
- How volume changes from changing dimensions
- Volume of a rectangular prism: word problem
- Volume word problems: fractions & decimals

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# Volume with fractional cubes

Another way of finding the volume of a rectangular prism involves dividing it into fractional cubes, finding the volume of one, and then multiplying that volume by the number of cubes that fit into our rectangular prism. Created by Sal Khan.

## Want to join the conversation?

- I don't understand how 1/4*1/4*1/4 equals 1/64. Doesn't timesing usually make the number bigger!?(25 votes)
- It usually does make things bigger but with fractions, it does not. Because 1x1x1 is equal to one and 4x4x4 is equal to 64. One is the numerator and 64 is the denominator. So it is 1/64. If 64 was the numerator then it would be bigger because 64/1 is equal to 64.(52 votes)

- I still do not understand the fact that if on of those small cubes is 1/4 ft and the volume is 1/4 cubic ft which is 1/64 cubic feet, why does it seem that the volume is less than the size of the cubes that are definitely smaller than the volume?(9 votes)
- Each small cube has a volume of 1/64 cubic feet. The prism as a whole has a volume of 1/4 cubic feet and:

1/64 < 1/4

Thus the prism has a greater volume than its constituent cubes as desired!(17 votes)

- I am still very confused and I've watched this video 3 times. I just still don't understand the steps that you need to do when doing these questions.(15 votes)
- Well, first you have to figure out the volume of one cube (e.g., 1/4*1/4*1/4=1/64), then you have to figure out how many cubes there are in the figure. Because the volume of one cube isn't one, you would then multiply the number of cubes by the volume of one cube. This way you would get the volume of the whole cube. Hope that helps!(5 votes)

- Ehhh.... I don't get this! Please help! I'm confused.(16 votes)
- I need help. I don't get how the video and the quiz don't even say the same thing(11 votes)
- I think this video will help get part of the quiz done.(7 votes)

- He is making it sound much more complex than it really is(10 votes)
- As I like to say, the more detailed the explanation, the more detailed the understanding.(6 votes)

- This does not make sense at all!! Joshua can you help me find the area of a prism well I mean can you tell me how to find an area of a prism?! :)(11 votes)
- 1/4 x 1/4 x 1/4 y tho just do 1/4 x 3(9 votes)
- 1/4 x 3 = 1/12, 1/4 x 1/4 x 1/4 = 1/64. This is because you multiply both the numerator and denominator together and then reduce if possible.(2 votes)

- I get the part of finding the volume but I still don't get how you find the amount of cubes of a certain measure that should be inside of a 3-Dimensional figure. I usually understand math, but this part really triggered me and I still don't know why or how.(7 votes)
- Yea, same it's sooo confusing and I'm failing the quizes on those questions. HELP!!(4 votes)

- How many cubes In lengths of a 1/4 pack(6 votes)

## Video transcript

So I have this
rectangular prism here. It's kind of the shape of
a brick or a fish tank, and it's made up of
these unit cubes. And each of these unit
cubes we're saying is 1/4 of a foot by 1/4 of
a foot by 1/4 of a foot. So you could almost
imagine that this is-- so let me write it
this way-- a 1/4 of a foot by 1/4 of a foot
by 1/4 of a foot. Those are its length,
height, and width, or depth, whatever
you want to call it. So given that,
what is the volume of this entire rectangular
prism going to be? So I'm assuming you've
given a go at it. So there's a couple of
ways to think about it. You could first think about
the volume of each unit cube, and then think about how
many units cubes there are. So let's do that. The unit cube, its
volume is going to be 1/4 of a foot times 1/4
of a foot times 1/4 of a foot. Or another way to think about
it is it's going to be 1/4 times 1/4 times 1/4 cubic
feet, which is often written as feet to the
third power, cubic feet. So 1/4 times 1/4 is
1/16, times 1/4 is 1/64. So this is going to be 1
over 64 cubic feet, or 1/64 of a cubic foot. That's the volume
of each of these. That's the volume of
each of these unit cubes. Now, how many of them are there? Well, you could view them
as kind of these two layers. The first layer has 1,
2, 3, 4, 5, 6, 7, 8. That's this first
layer right over here. And then we have the
second layer down here, which would be another 8. So it's going to
be 8 plus 8, or 16. So the total volume
here is going to be 16 times 1/64
of a cubic foot, which is going to be equal to
16/64 cubic feet, which is the same thing. 16/64 is the same thing as 1/4. Divide the numerator and
the denominator by 16. This is the same thing
as 1/4 of a cubic foot. And that's our volume. Now, there's other ways that
you could have done this. You could have just thought
about the dimensions of the length, the
width, and the height. The width right over here
is going to be 2 times 1/4 feet, which is
equal to 1/2 of a foot. The height here
is the same thing. So it's going to be 2
times 1/4 of a foot, which is equal to 2/4,
or 1/2 of a foot. And then the length here
is 4 times 1/4 of a foot. Well, that's equal to 4/4 of a
foot, which is equal to 1 foot. So to figure out
the volume, we could multiply the length times
the width times the height, and these little dots here,
these aren't decimals. I've written them
a little higher. These are another way. It's a shorthand
for multiplication, instead of writing this
kind of x-looking thing, this cross-looking thing. So the length is 1. The width is 1/2 of
a foot, so times 1/2. And then the height
is another 1/2. Let me do it this way. The height is another 1/2, so
what's 1 times 1/2 times 1/2. Well, that's going
to be equal to 1/4. And this is a foot. This is a foot. This is a foot. So foot times foot
times foot, that's going to be feet to the
third power, or cubic feet. 1/4 of a cubic
foot, either way we got the same result,
which is good.