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DRILL (A) Name the cross-sections you would find in a cone, cylinder, cube, rectangular prism.

DRILL (A) Name the cross-sections you would find in a cone, cylinder, cube, rectangular prism. (B) What solids would you use to model these farm structures? Why would we want to know?. What would you get if you turned these shapes about their axes?. Rotating Triangle in 3D.

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DRILL (A) Name the cross-sections you would find in a cone, cylinder, cube, rectangular prism.

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  1. DRILL (A) Name the cross-sections you would find in a cone, cylinder, cube, rectangular prism. (B) What solids would you use to model these farm structures? Why would we want to know?

  2. What would you get if you turned these shapes about their axes?

  3. Rotating Triangle in 3D Axis bisects triangle Rotation creates a cone

  4. Triangle: Axis Along Edge Edge along axis forms center axis of solid Other edges create curved surfaces

  5. Rectangle: Axis Bisecting Edges perpendicular to axis draw flat faces Edges parallel to axis draw curved surfaces Rotation creates: cylinder

  6. Rectangle: Axis Along Edge Edges perpendicular to axis draw flat faces Edges parallel to axis draw curved surfaces Rotation creates: cylinder

  7. Circle: Axis Bisecting Curved edges draw curved surfaces Rotation creates: sphere

  8. Circle: Axis Along Edge Curved edges draw curved surfaces Rotation creates: torus

  9. What is VOLUME?

  10. Why does V = B x h calculate the volume of prisms & cylinders? How do you know you can trust the formulas? h V = B x h B

  11. Cavalieri Principle If cross-sectional area of two prisms is the same for every height above the base, then the volumes will be the same. Bonaventura Cavalieri

  12. Cavalieri’s Principle

  13. Cylinder: US Quarter h = .7in B = 2.86in2

  14. Stack of 16 quarters V = 2.86 x11.2=32 in3 B = 2.86in2 h = 11.2 in

  15. Works for unusual shapes If base area is congruent, multiply B x h to easily calculate volume. height

  16. Right & Oblique Prisms & Cylinders

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