what is the volume of the composite figure? 1,200 units3 4,400 units3 5,040 units3 6,000 units3 This is a topic that many people are looking for. bluevelvetrestaurant.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, bluevelvetrestaurant.com would like to introduce to you Volume of Composite Figures. Following along are instructions in the video below:
Guys. Its miss perry and today were going to talk about the volume volume of composite figures composite just means that theres more than one thing that it up so a composite figure means. Its going to be more than just a cylinder or more than just a sphere.
Well have two or more shapes put together to make a figure. Okay so were gonna use three point one four four pi. Were gonna round our answers to the nearest tenth okay the first thing we need to do when we see a shape thats not just a regular cylinder or a cone or a cylinder is we need to identify those things that make up that shape so.
When i look at this here. This is our problem that were going to be working on first. I see a cylinder on the bottom.
And then i also see whats called a hemisphere on top so a hemisphere. Just means half of a sphere. Its like the top half of a sphere.
So okay so first thing. I see is a hemisphere and this sphere and the second thing. I see is a cylinder and those are the two figures that make up this entire shape okay once i know and we have to know what the shapes are so we know which formulas to use to find volume so the first thing.
Were going to work on is were going to work on the hemisphere. So we have to remember the volume of a sphere since its a hemisphere. Well start with the volume of a sphere and we talked about this earlier that the volume of a sphere is four times pi times the radius to the third power.
Then we divide everything by three now because this is only half of a sphere. Not the whole sphere. When were done with all of that we have to divide by two okay so when were done well just divide everything by two then i have the volume of this top section right here.
Okay. Now no we need to use radius. But they didnt give us radius.
They gave us the diameter. So the radius is going to be twelve divided by two which in this case is going to be six. It just so thats what were going to use right here.
This is what were going to use for our radius. All right. So lets play it in our.
Numbers so the volume here is going to be four times 314. Times. The radius in this case is six to the third power.
Then were going to divide everything by three okay then when were done with that were going to divide everything by two so thats a lot for me to have to remember when i go into my calculator. But i think i can remember it okay so heres our calculator. So we had a radius of six.
So that was to the third power six to the third power its 216. Were gonna multiply by pi and thats the number we get and were gonna multiply by four thats what we get and we wrote the whole thing when were done is divided by three now thats great if we were doing a whole sphere. But remember its a hemisphere and weve got to divide it in two so what im gonna do for this special calculator is that and then it divides.
It by two for me. Thats why i like this calculator app its pretty cool and that makes our volume of our. Hemisphere 450.
22 because were gonna round to the nearest tenth for 150 22. Cubic inches. So if you look at what we have on the next page here thats what we have right up at the.
Top there is 450 22. Cubic inches. Okay so thats how i got that now were gonna work on the volume of the cylinder.
Now weve got to remember the volume of a cylinder volume of a cylinder is the value of the area of the base which in this case is a circle. So that was pi r squared. And then we have to multiply by the height of the cylinder okay so times the height our radius is going to be the same radius.
Because the sphere and the cylinder share the same circle part right here so our radius. In this problem is going to be not 12. But 12 divided by 2 again.
Which is 6 inches. And our height of our cylinder. Is 13 inches.
So those are the numbers. Were going to plug in all right so we get a volume of the cylinder is 314. Times our radius squared.
6. Squared. Times our height of 13 and well get our volume of the cylinder.
All right. So lets go to our calculator new problem. Lets clear it so we have 6 squared.
Its our radius squared times. Pi. Thats the area of that circle and then were going to multiply by the height.
Which was 13 and we get 1469 point. 5 cubic inches. So if you look at my next screen.
Ah. Thats what i have up here. Weve got 1469 point.
5. Cubic. Inches.
Once i have those separate volumes. Figured out all we have to do is add them. Together so were going to add these two numbers together 452.
02. 1416. 95.
Just so you guys know i dont always use a calculator here. We go so theres seven and eleven. And that makes twelve and thats nine and thats one so the volume of our composite figure.
All together is 1921 a point seven cubic inches. All right so thats how we find the volume of a composite figure all right so lets try another one. Yeah this one looks a little bit different so still going to use 314 for pi and were still going to round our answers to the nearest tenth.
What shapes do you guys see here what different ones make up this figure. Oh wait all right did you find him on top. We have a cone and on the bottom.
We have a cylinder. So those are the two shapes that were going to four figures that were gonna find the volume of okay. So lets start with the cone now i got to remember the volume of a cone is this one ones might be a little bit harder for you to remember.
Its pi r. Squared. Times the height of the cone now that looks like a cylinder.
Which it was and then when we were all done we divided by three thats how you find a cone remember. A cone is 1 3. The volume of a cylinder.
And so the 1 3. Means. Were going to divide by 3.
Now remember this height right here is 4. That height right there the height of the cone. So our radius.
Luckily they gave us the radius this time so our radius is 7 feet. But the height that were going to use is also 7 feet. Because thats the height of the cone.
Okay cuz everything. Were doing right now is for the cone. So.
This is also seven feet all right so lets get calculating. Alright. So the volume here is gonna be 314.
Times. Our radius seven squared times. The height.
Which is also seven and when were all done. Were gonna divide by three all right so pi r. Squared h.
Divided by three right there okay clear out that so our radius was seven. So seven squared forty nine. Yeah i got that right times pi.
Theres pi r. Squared. Times the height.
Which was seven okay and then were going to take the whole thing and divide by three so the volume that we get for that cone is 359. This is point zero zero six. So well use three hundred fifty nine point zero for the volume of the cone right there so three hundred fifty nine point zero cubic feet.
And then were going to find the volume of the cylinder. Thats on the bottom. So.
A volume of a cylinder is pi. R. Squared h.
Now this h is a different age this h. Is not because were not looking at the cone. Were looking at the cylinder down here.
Its the height of the cylinder. Now they share this same circle. So the radius is going to be the same so the radius.
Were going to use is still seven feet. Thats because they share that one part. But the height is going to be the height of the cylinder this time because this is what were looking at so the height.
Were going to use is six feet all right and then were going to put those numbers in. So our volume is 314. Times our radius squared seven squared times the height.
Which is six all right so. Weve got pi r squared. And h.
Pi r. Squared h. And well clear this.
So well start with our seven. Squared. 49 oops times 314.
Times. The height and remember this time at six. Its not seven and we get nine hundred twenty three point two if we round to the nearest tenth.
So nine hundred twenty three point two is just what i have up here. See that so now all we have to do is add those two pieces together. So lets add them together.
So i have three hundred fifty nine point zero nine hundred twenty three point two. We add those up to i get 12 carry the 1 6. 2 is.
8 and that makes. 12 so our final. Volume its 1280 22.
Cubic feet. Thats how you find the volume of composite figures. So make sure we separate them into their parts identify what shapes they are so its kind of like two problems in one hmm thats kind of what it is see its like a deal.
Its a bargain you get a two for one all right. Thats it for now talk to you later guys bye. .
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