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Exercise

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

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Exercise

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

  3. Exercise 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.

  4. 12 Exercise What would the calculation of bhH give? the volume of a triangular prism

  5. h h w w l l

  6. 13 V = BHThe volume of a pyramid or cone(V) is equal to one- third the area of the base (B) times the height (H). Formula: Volume of a Pyramid or a Cone

  7. 13 13 V = BH 12 cm = (82)(12) 8 cm 8 cm Example 1 Find the volume of the square pyramid. = 256 cm3

  8. V = BH = p(42)(6) 13 13 Example 2 Find the volume of the cone. 6 cm = 32p = 32(3.14) 4 cm ≈100.5 cm3

  9. Example What is the volume of a pyramid if its height is 10 units and its base is 8 units by 12 units? 320 units3

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

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

  12. Example What would happen if all the dimensions were doubled? The volume would be multiplied by a factor of 23 = 8.

  13. Example What is the volume of a square pyramid if each side of its base is 6 units and its height is 5 units? 60 units3

  14. Example 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 22 = 4.

  15. 43 43 V = pr3 The volume of a sphere (V) is equal to the product of , p, and the radius cubed (r). Formula: Volume of a Sphere

  16. 152 r = = 7.5 ft. Example 3 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.)

  17. 43 43 43 V = pr3 = p(7.53) = p(421.875) 1,687.53 = p Example 3 ≈ 1,766.25 ft.3

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

  19. 43 43 43 34 34 V = pr3 pr3 = 288p ( ) pr3 = (288p) Example 4 Find the radius of a sphere with a volume of 288p m3.

  20. Example 4 pr3 = 216p r3 = 216 r = 6 m

  21. Example What is the volume of a sphere with a radius of 6 units? 904.32 units3

  22. Example A city needs a 10,000 m3 water tower for its increasing population. What should the radius be if the water tower is in the form of a sphere? 13.37 m

  23. Exercise 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.

  24. Exercise 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.

  25. V = pr2H + pr2H = p(92)(16) + p(92)(5) 13 13 ( ) 0.8 bu.1 ft.3 = 1,431p ft.3 Exercise = 1,296p+ 135p = 1,431p ft.3 ≈ 3,595 bu.

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