Volume of composite solids
About this video
The video finds the volume of a composite solid by splitting it into two rectangular prisms. A 1/2 m cube has volume 1/8 cubic meter and a 1 m by 1/2 m by 3/4 m prism has volume 3/8 cubic meter, so the total is 4/8 = 1/2 cubic meter.
You'll be able to
- break a composite solid into rectangular prisms.
- find missing dimensions by using other lengths in the figure.
- multiply fractions to find each volume and add them for the total.
Key words
- volume
- The amount of space a solid takes up, measured in cubic units.
- rectangular prism
- A box-shaped solid; its volume is width x depth x height.
- cube
- A rectangular prism whose width, depth and height are all equal.
- cubic meter
- The volume of a cube that is 1 meter on each side.
Transcript
- [Instructor] What I would like to do is figure out the volume of this figure here. And if you are inspired, please pause the video and try to work through this on your own before we do it together. Alright, now let's work through this together. So we know how to find the volume of rectangular prisms.
And this isn't exactly a rectangular prism, but maybe we can break it up into rectangular prisms and then add everything together. And there's two ways we could break it up. We could break it up into, let's we see, we can make this, let me see if I can draw it so we can see it clearly.
We could break it up this way. So we have this thing that at least looks like a cube. We'll figure out if it actually is a cube, and then this other rectangular prism. And we could separately figure out their volumes and then add them up. Another way to break it up could be to have it as two rectangular prisms.
One that looks like this on the bottom and then one on the top. But let's go with the first way. If you want, you could solve it the other way and see that you will, you should get the same answer. So let's first figure out the dimensions of this cube right over here, or what looks like a cube.
I don't wanna jump the gun and assume it's a cube. You should never just assume based on how things look. So we see it's height is 1/2 meters. Now what is its depth? Well, this length is the same as this here, which is also 1/2 meters. 1/2 meters. And what's this width right over here?
Well, that's going to be this 1 1/2 meters, which is this whole width of the whole figure minus this one meters up here. So that is also going to be 1/2 meter. So this thing in orange that I'm highlighting is indeed a cube. And its dimensions are half a meter times half, or its volume is gonna be 1/2 meter times 1/2 meter, times 1/2, which is going to be equal to 1/2 times 1/2 is 1/4 times 1/2 is 1/8 cubic meters.
So that's the orange part. We are not done. We now wanna figure out the volume of this other rectangular prism right over here. Now what are its dimensions? Well, we could see it's width, right over here is one meter. So one meter times its depth, which is 1/2 meter times 1/2 meter, times its height times this 3/4 meter.
3/4 of a meter. And what's that going to be equal to? Well, one times 1/2 is just 1/2 and 1/2 times 3/4 is 3/8. So it's gonna be 3/8 of a cubic meter. And so what's going to be the total volume of the entire figure? Well, we just have to add the 1/8, sorry, 1/8 of a cubic meter to the 3/8 of a cubic meter, which of course is equal to 1/8 plus 3/8 is 4/8 of a cubic meter, which is the same thing as 1/2 of a cubic meter.
And we are done.
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