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### Course: Geometry (all content)>Unit 8

Lesson 2: Volume with fractions

# 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.
(57 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.
(17 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!
(8 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?
(10 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!
(19 votes)
• Ehhh.... I don't get this! Please help! I'm confused.
(17 votes)
• I need help. I don't get how the video and the quiz don't even say the same thing
(12 votes)
• I think this video will help get part of the quiz done.
(8 votes)
• He is making it sound much more complex than it really is
(12 votes)
• As I like to say, the more detailed the explanation, the more detailed the understanding.
(7 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?! :)
(14 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.
(8 votes)
• Yea, same it's sooo confusing and I'm failing the quizes on those questions. HELP!!
(5 votes)
• 1/4 x 1/4 x 1/4 y tho just do 1/4 x 3
(9 votes)
• I don't think you can do that because you have to multiply 1/4 x a second 1/4 x a third 1/4. That is what I think but I could be wrong.
(3 votes)
• How many cubes In lengths of a 1/4 pack
(7 votes)

## Video transcript

- [Instructor] 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, this is a fourth 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 unit 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 1/64 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 one, two, three, four, five, six, seven, eight. That's this first layer right over here. That's this first layer right over here. And then we have the second layer down here, which would be another eight. So it's going to be 8 plus 8 or 16. So the total volume here, the total volume is going to be 16 times 1/64 of a cubic foot, which is going to be equal to 16/64. 16/64 cubic feet, 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, 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 two times 1/4 feet, which is equal to one half of a foot. The height here is the same thing, it's two times, so it's gonna be two times 1/4 of a foot, which is equal to 2/4 or 1/2 of a foot. And then the length, the length here is 4 times 1/4 of a foot. 4 times 1/4 of a foot, well, that's equal to 4/4 of a foot, which is equal to one foot. So to figure out the volume, we could multiply. We could multiply the length times the width, the length times the width times the height. Times the height, and I mean 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 a, this kind of X looking thing, this cross looking thing. so the length is one, the width is half of a foot, so times one half. And then the height is another half. Let me do it this way. The height is another half. 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 gonna 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.