Problem 4 Finding the Volume of an Oblique Cone

What is the volume of the oblique cone below? Give your answer in terms of π and also rounded to the nearest cubic foot.

V = 1 3 π r 2 h Use the formula for volume of a cone.   = 1 3 π ( 15 ) 2 ( 25 ) Substitute  15  for  r  and  25  for  h .   = 1875 π Simplify.   ≈ 5890.486225 Use a calculator. table with 4 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 volume of a cone. , row2 column 1 , , column 2 equals , column 3 1 third , pi . open 15 , close squared . open 25 close , column 4 cap substitute . 15 , for , r , and , 25 , for , h . , row3 column 1 , , column 2 equals , column 3 1875 , pi , column 4 cap simplify. , row4 column 1 , , column 2 almost equal to , column 3 5890.486225 , column 4 cap use a calculator. , end table

The volume of the cone is 1875 π ft 3 , 1875 , pi , ft cubed , comma  or about 5890 ft 3 . 5890 . ft cubed , .

✓ Got It?

4. 1. What is the volume of the oblique cone below in terms of π and rounded to the nearest cubic meter?

      

   2. Reasoning How does the volume of an oblique cone compare to the volume of a right cone with the same diameter and height? Explain.

✓ Lesson Check

Do you know HOW?

What is the volume of each figure? If necessary, round to the nearest tenth.

Do you UNDERSTAND?

3. Compare and Contrast How are the formulas for the volume of a pyramid and the volume of a cone alike? How are they different?
4. Error Analysis A square pyramid has base edges 13 ft and height 10 ft. A cone has diameter 13 ft and height 10 ft. Your friend claims the figures have the same volume because the volume formulas for a pyramid and a cone are the same: V = 1 3 B h . v equals , 1 third b h .  What is her error?