Geometry – Cones, Spheres, and Cylinders

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     Cones, spheres, and cylinders are not polyhedrons. These figures have curved surfaces, not flat faces.

 Cylinders

     Cylinders are similar to prisms.  The difference, though, is that its two bases are circles, not polygons.  The sides of a cylinder are different from the sides of a prism because the sides of a cylinder are curved, not flat. 

     Cylinders have parallel congruent bases, but their bases are circles, not polygons. We can find the volume of a cylinder in the same way that we find the volume of a prism.   The volume is the base time the height (V=bh).

     Since the base of a cylinder is always a circle, we can substitute the formula for the area of a circle into the formula for the volume. 

     That is:

V = πr²h

Cones

     Cones have one circular base and a vertex that is not located on the base.  Cones are similar to pyramids because they both have just one base and they meet at the vertex.  Since the base area is a circle, again we can substitute the area formula for a circle into the volume formula, in place of the base area.

     That is:

V = 1/3 πr²h

Spheres

     A sphere has all of its points at an equal distance from the center point.   Like a circle, a sphere has a radius and a diameter.

     The formula for finding the volume of a sphere is:

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