1. Exercise If a pyramid and a cone have bases with the same area and altitudes that are equal, are their surface areas equal? no

2. If a pyramid and a cone have bases with the same area and altitudes that are equal, are their volumes equal? yes Exercise

3. In this text, what is the difference between h and H? h = length of the altitude of a plane figure and H = length of the altitude of a solid figure. Exercise

4. What would the calculation of bhH give? the volume of a triangular prism 1212 1212 Exercise

5. h h w w l l h h w w l l

6. Formula: Volume of a Pyramid or a Cone V = BHThe volume of a pyramid or cone (V) is equal to one- third the area of the base (B) times the height (H). 1313 1313

7. Find the volume of the square pyramid. = 256 cm 3 V = BH 1313 1313 = (8 2 )(12) 1313 1313 8 cm 12 cm Example 1

8. Find the volume of the cone. ≈ 100.5 cm 3 V = BH 1313 1313 =  (4 2 )(6) 1313 1313 = 32  = 32(3.14) 6 cm 4 cm Example 2

9. What is the volume of a pyramid if its height is 10 units and its base is 8 units by 12 units? 320 units 3 Example

10. What would happen to the volume of the pyramid in the previous question if its length were doubled? The volume would be doubled. Example

11. What would happen to the volume if any single dimension were doubled? Example The volume would be doubled.

12. What would happen if all the dimensions were doubled? The volume would be multiplied by a factor of 2 3 = 8. Example

13. What is the volume of a square pyramid if each side of its base is 6 units and its height is 5 units? 60 units 3 Example

14. What would happen to the volume of the pyramid in the previous question if the sides of the square base were doubled? The volume would be multiplied by a factor of 2 2 = 4. Example

15. Formula: Volume of a Sphere V =  r 3 The volume of a sphere (V) is equal to the product of, , and the radius cubed (r). 4343 4343 4343 4343

16. Find the volume of a sphere with a diameter of 15 ft. to the nearest hundredth. Find the number of gallons it will hold. (1 ft. 3 = 7.48 gal.) r = = 7.5 ft. 15 2 Example 3

17. V =  r 3 4343 4343 =  (7.5 3 ) 4343 4343 =  (421.875) 4343 4343 =  1,687.5 3 ≈ 1,766.25 ft. 3 Example 3

18. ≈ 13,212 gal. 7.48(1,766.25) Example 3

19. Find the radius of a sphere with a volume of 288  m 3. V =  r 3 4343 4343  r 3 = 288  4343 4343  r 3 = (288  ) 4343 4343 3434 3434 ( ) 3434 3434 Example 4

20.  r 3 = 216  r 3 = 216 r = 6 m Example 4

21. What is the volume of a sphere with a radius of 6 units? Example 904.32 units 3

22. A city needs a 10,000 m 3 water tower for its increasing population. What should the radius be if the water tower is in the form of a sphere? Example 13.37 m

23. A grain storage bin is a steel cylinder with a conical top. One company markets a bin that is 18’ in diameter, 16’ high at the eaves, and 21’ high at the peak. Exercise

24. What is the maximum number of bushels of wheat (rounded to the nearest bushel) that can be stored in the bin? There are 0.8 bushels in one cubic foot. Exercise

25. V =  r 2 H +  r 2 H 1313 1313 = 1,296  + 135  = 1,431  ft. 3 =  (9 2 )(16) +  (9 2 )(5) 1313 1313 = 1,431  ft. 3 0.8 bu. 1 ft. 3 ( ) ≈ 3,595 bu. Exercise