When the base and height of a right cone and a right cylinder are the same, the volume of the right cylinder is three times the volume of the right cone. Alternatively, when the base and height of a right cone and a right cylinder are the same, the volume of the right cone is the volume of the right cylinder.

Key Lesson Marker

 

In general, the volume formula for any right cone is

r is the radius of the circular base
h is the height

 

Example 2

What are the volumes, to the nearest tenth, of the right cone and related right cylinder?

Step 1: Assign variables to the given values.
Let r = 3.25 dm, h = 5.75 dm

Step 2: Substitute the given values into the formulas for the volume of a right cone and the volume of a right cylinder.

Step 3: State the answer with the appropriate units.
The volume of the right cone is approximately 63.6 dm3 and the volume of the right cylinder is approximately 190.8 dm3.

For another example of how to determine the volumes of a right cylinder and a right cone see p. 82 of Mathematics 10.