Take note Theorem 11-9: Volume of a Cone

The volume of a cone is one third the product of the area of the base and the height of the cone.

V = 1 3 B h ,  or  V = 1 3 π r 2 h v equals , 1 third b h comma , or , v equals , 1 third , pi , r squared , h

Problem 3 Finding the Volume of a Cone

Traditional Architecture The covering on a tepee rests on poles that come together like concurrent lines. The resulting structure approximates a cone. If the tepee pictured is 12 ft high with a base diameter of 14 ft, what is its approximate volume?

V = 1 3 π r 2 h Use the formula for the volume of a cone.   = 1 3 π ( 7 ) 2 ( 12 ) Substitute  14 2 ,  or  7 ,  for  r  and  12  for  h .   ≈ 615.7521601 Use a calculator. table with 3 rows and 4 columns , row1 column 1 , v , column 2 equals , column 3 1 third , pi , r squared , h , column 4 cap use the formula for the volume of a cone. , row2 column 1 , , column 2 equals , column 3 1 third , pi . open 7 , close squared . open 12 close , column 4 cap substitute . 14 over 2 , comma . or , 7 comma , for , r , and , 12 , for , h . , row3 column 1 , , column 2 almost equal to , column 3 615.7521601 , column 4 cap use a calculator. , end table

The volume of the tepee is approximately 616  ft 3 . 616 . ft cubed , .

✓ Got It?

3. 1. The height and radius of a child's tepee are half those of the tepee in Problem 3. What is the volume of the child's tepee to the nearest cubic foot?
   2. Reasoning What is the relationship between the volume of the original tepee and the child's tepee?