Relationship Between the Volume of a Cylinder & a Cone

T.i.P.S.

Students must be able to describe and show the relationship between cylinders and cones as it relates to volume. Both shapes have the same size bases and heights. They must understand how the formula connects to the modeling and/or demonstration (i.e. if it takes the volume of 3 cones to fill a cylinder with the same base and height the formula for the cone is one-third the volume of the cylinder.

Example

The radius of the cylinder shown below is 6 in and the height is 10 in. 

 Mrs. Smith took a cone with the same radius and the same height as the cylinder. Which of the following is true about the relationship?    a) It takes the volume of two cones to fill the cylinder.
   b) It takes the volume of three cones to fill the cylinder.
   c) It takes the volume of three cylinders to fill the cone.
   d) There is no relationship between the two figures.

Hint
Possible Solution

TEKS

8.6 Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to:

 (B) model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas

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