The volume of a cone is the number of unit cubes, or cubic units, needed to fill the cone. The formula for the volume of a cone is 1 third the product of the base area and the height of the cone.
This cylinder and cone have the same height. They also have the same radius, so the area of their bases is the same. If you mark the cylinder in thirds, you can pour the contents of the cone into 1 third of the cylinder.
Example Finding Volumes of Cones
What is the volume of each cone in terms of π?
a.
b.
c.
Solution
Use v equals , 1 third , pi , r squared , h to find the volume of a cone.
a. table with 3 rows and 2 columns , row1 column 1 , v , column 2 equals , 1 third , pi , r squared , h , row2 column 1 , , column 2 equals , 1 third , pi . open 3 close squared . open 3 close , row3 column 1 , , column 2 equals 9 pi , end table
The volume of the cone is about 9π cm^{3}.
b. table with 3 rows and 2 columns , row1 column 1 , v , column 2 equals , 1 third , pi , r squared , h , row2 column 1 , , column 2 equals , 1 third , pi . open 2 close squared . open 7 close , row3 column 1 , , column 2 almost equal to , 9.33 , pi , end table
The volume of the cone is about 9.33π cm^{3}.
c. table with 3 rows and 2 columns , row1 column 1 , v , column 2 equals , 1 third , pi , r squared , h , row2 column 1 , , column 2 equals , 1 third , pi . open 1.5 close squared . open 10 close , row3 column 1 , , column 2 almost equal to 7.5 pi , end table
The volume of the cone is about 7.5π cm^{3}.