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Today’s Class :

Learn about Cavalieri's Principle and apply formulas to calculate volumes and surface areas of prisms and cylinders in geometry class today. Explore cross-sections, bases, and heights of various solids to find their volumes accurately. Practice with assigned homework and review materials.

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Today’s Class :

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  1. Today’s Class: Problem of the Day Cavalieri’s Principle Volume of a Prism Volume of a Cylinder HW: Pg.513, Q7-20

  2. Problem of the Day Formulae: LA = p • h TSA = LA +2B Area of B = ½ap 10 • Find • The Lateral Surface Area • The Total Surface Area 3 5

  3. h h Cavalieri’s Principle If 2 solids have the same vertical height, and if the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the 2 solids have the same volume.

  4. Volume? 2 3 6

  5. Volume of Rectangular Prism Area of Base x height = length x width x height B h = l w h h w l

  6. Any Prism V = B h 3 4 B = ½ (3 x 4) = 6 h = 3 V = 6 (3) = 18 3 5

  7. Volume? V = B h = (2 x 4) x (3) = 24 = (2 x 3) x (4) = 24 = (3 x 4) x (2) = 24 3 2 4

  8. Volume? 15 9 12

  9. Volume? Bases are Isosceles trapezoids 2 B = ½ (4) (2 + 8) = 20 h = 3 V = 20 (3) = 60 5 3 4 8

  10. Volume of Cylinder V = B h B =  r2 V =  r2 h Not same as prism! height radius Volume = (area of Base) x height same as prism!

  11. Area and Volume? TA = LA + 2B LA = 2  r h = 2  (4) (8) = 64  B =  r2 = 16  TA = 64  + 32  = 96  V = B h = 16  (8) = 128  8 r = 4

  12. Volume? 2 2 ½

  13. Find the volume: Formulae: V = B • h Area of B = ½ap 10 3 5

  14. Today’s Class: • Problem of the Day • Review Slides • Worksheet HW: Finish Review Worksheet

  15. Problem of the Day: Find the Total Surface Area AND the volume 9 6 25

  16. Find the Total Surface Area AND the Volume 10 4 15

  17. Find the Total Surface Area AND the volume 36 6

  18. Review Worksheet

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