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Agenda for today

Agenda for today. New Solids: CYLINDERS, PYRAMIDS, CONES, SPHERES Challenge Questions Projects and exam area next week! Sites: 1 , 2 , 3 , mathsnacks.org Videos (Bubbles is #2): 1 , 2. Solids: Cylinders. Have 2 identical faces (bases) The two bases are circles

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Agenda for today

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  1. Agenda for today New Solids: CYLINDERS, PYRAMIDS, CONES, SPHERES Challenge Questions Projects and exam area next week! Sites: 1, 2, 3, mathsnacks.org Videos (Bubbles is #2): 1, 2

  2. Solids: Cylinders Have 2 identical faces (bases) • The two bases are circles • The two bases lie in parallel planes

  3. Solids: Cylinders (cont'd) Do not have lateral faces; instead there is one, big rectangle wrapped around connecting the bases SIXTH PROBLEM SET (from last time)

  4. Solids: Cylinders (cont'd) Recall the formula for SA of a prism Compare it to our cylinder formula

  5. Solids: Cylinders (cont'd) Recall the formula for V of a prism Compare it to our cylinder formula

  6. Cylinders TASKS Label a cylinder’s height and radius Find the surface area of a prism Find the volume of a prism SEVENTH PROBLEM SET

  7. Solids: Cylinders (cont'd) Discussion question: • Which cylinder makes a better container?

  8. Solids: Pyramids

  9. Pyramids (continued) Have a polygon for a base Have triangles that join the base to the apex Have some tricky terminology…

  10. Pyramids (continued) Height (also known as altitude) is the perpendicular distance between base and apex Slant height is the distance between the apex and the center of the base’s edge

  11. FIRST PROBLEM SET

  12. Pyramids (continued) Here is the surface area formula: P is perimeter of the base S is slant height BA is area of the base

  13. Pyramids (continued) Here is the volume formula: BA is area of the base H is height (or altitude)

  14. Pyramids TASKS Correctly label a pyramid’s apex, base, height, and slant height Find the surface area of a square pyramid Find the volume of a square pyramid SECOND PROBLEM SET

  15. Solids: Cones

  16. Cones (continued) Have a circle for a base Have an apex Have both height and slant height

  17. “In projective geometry, a cylinder is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

  18. Cones (continued) Here’s the formula for surface area: “r” is radius of the base “S” is slant height

  19. Cones (continued) Here’s the formula for volume: “H” is height (or altitude)

  20. Cones TASKS Correctly label a cone’s apex, base, height, and slant height Find the surface area of a right cone Find the volume of a cone THIRD PROBLEM SET

  21. Solids: Spheres

  22. Spheres (continued) Have a radius Have the other Circle stuff

  23. Come up with the formula for SA…

  24. Spheres (continued) Here is the surface area formula: (This formula wierds me out: why is it so simple?)

  25. Spheres (continued) Here is the volume formula: (notice that r is cubed) FOURTH PROBLEM SET

  26. Spheres TASKS Find the surface area of a sphere Find the volume of a sphere Work with combinations FIFTH PROBLEM SET

  27. Challenge Questions Why do elephants have big ears? Seven Bridges of KonigsbergLink Predict the Mobius strip’s split Link

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