The volume of a cone

​​A cone or a cup? ​Which ever is bigger, of course. The volume of a cylinder is explained in another video. Now, it's time for a cone. A cone is not only a tasty way to serve ice cream, but also a geometric shape, so let's calculate the volume of a cone. If you've seen the video on pyramids, you know that you get the volume of a pyramid by calculating the area of the base times the height divided by 3, and a pyramid can appear in many different forms.

The base can be three-sided trihedron, four-sided tetrahedron, or it can have any number of sides. The more sides a pyramid has, the closer its shape approaches that of a cone, so you calculate the volume of a cone exactly the same way - the area of the base times the height divided by 3. The only difference is that the base of a cone is round, so you'll have to use the formula for the area of a circle to calculate the area of the base. ​ ​The area of the base is Pi times radius squared, times height divided by 3. We usually draw cones standing on the base. In order to avoid dropping the ice cream, we turned it upside down.

The radius is 4 centimeters. The height is 12 centimeters. Pi is approximately 3,14. Four squared times Pi times 12 divided by 3; that's 201 cubic centimeters, or roughly 2 deciliters of ice cream. The volume of a cone, the area of the base times the height divided by 3.

We'll cover the calculation of the volume of ice cream scoops and the surface area of a cone another time.