Finding VOLUME for Cones and Pyramids!
Cones and pyramids are fun shapes to explore! They actually have the SAME formula too! Wow! That's because a pyramid is a type of cone! But for our lesson we're going to be looking at circular cones.
A CIRCULAR CONE is a cone with a circular base. A CONE is a 3D shape that has a base and slanted sides that meet in a single vertex. When you think of a cone, you probably think of an ice cream cone! This is a circular cone, and is what we will use for our formula. |
Watch this video to the side as we discover the relationship between circular cylinders, and circular cones! Make sure you pause before we get to the examples, cones and pyramids are much easier to do together with video! We're going to discover together why the volume for a circular cone is:
V = 1/3 πR^2 x height Do you see the relationships? Great! Now press play again and try the examples for yourself. What answers did you get? How did you get them? Well done! |
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Here's another picture to help see that relationship we talked about. We use the 1/3 because it would take 3 cones to fill up our cylinder, as long as they have the same size and shape base!
The same can be said for pyramids, but instead of circular cylinders, we have to use triangular cylinders! Why? Let's fine out! |
A PYRAMID is a special type of cone that has a flat base and faces that slope up to a vertex at the top! They're named, like cones, by the shape of their base! We can have square based pyramids, triangular based pyramids, and more! In our video, we're going to look at triangular based pyramids! But guess what? The volume formula is still the same! It changes, just like cylinders, depending on the base.
For a triangular based pyramid, it would be 1/3 the area of a triangle, multiplied by the height! |
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Let's look at this relationship in our video, using water and shapes again! It's easy to see that our formula is always 1/3 of the area of the base, multiplied by the height, because it takes 3 pyramids to fill a cylinder with the same base shape and size!
Don't forget to pause before seeing the answer so that you can give this formula a try by yourself! Were you able to get the same answer that I did? Fantastic! Now see if you can draw your own cones and pyramids! |