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Keywords: Volume, Cone Derive volume formula, Cylinder,Volume Cylinder,Geometry, Math
Common Core Standard: 8GC9 "Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems."
Video Summary: Why is the volume of a cone equal to 1/3πr^2h, and the volume of a cylinder πr^2h. In other words, why does it take three cones to fill up one cylinder? The video first works an example volume problem involving an equal sized cone and cylinder. The volume of the cone works out to be exactly 1/3 the volume of the cylinder.
Next, real geometric shapes are used to demonstrate this fact. Again an equal sized cylinder and cone are used. The cone is filled up with water, and then poured into the cylinder. According to the volume formula it should take exactly three of these cones to fill one cylinder. When the third cone is poured into the cylinder the water fills the cylinder completely. Hopefully this video will help you have a little better understanding of the formulas for the volume of cones and cylinders.
Demonstration: Volume of a Cone and Cylinder
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Demonstration: Volume of a Cone and Cylinder