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Now, tell me what the concept is:

In silence, look at the following images… please do not discuss your ideas until you are asked to share. Now, tell me what the concept is:. Pyramids! (you guys are so smart… now try another one…) (Please remember to stay quiet until I ask you to share what you think.).

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Now, tell me what the concept is:

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  1. In silence, look at the following images… please do not discuss your ideas until you are asked to share.

  2. Now, tell me what the concept is: Pyramids! (you guys are so smart…now try another one…) (Please remember to stay quiet until I ask you to share what you think.)

  3. Now, tell me what the concept is: Cones! (so smart again…I knew you could do it.)

  4. GEOMETRY Mr. Owh Today is: Tuesday, February 13th, 2007 Lesson 12.3 – Surface Area of Pyramids & Cones NC 27A, 27B, 28A, 28B Announcements: Quiz for 12.1 – 12.3 is this Thursday (2/15) You will need a calculator for this chapter

  5. Lesson 12.3 – Surface Areas of Pyramids & Cones • Today’s Objectives: • Find the surface area of a pyramid. • Find the surface area of a cone. • Today’s Key Terms: pyramid, regular pyramid, slant height, lateral face, cone, circular cone, right cone, lateral surface • Materials Needed Today:notebook, geometer/ruler, calculator • Today’s Geometry Standard: 8, 9

  6. Hexagonal Pyramid ABCDEF V > V is the vertex of the pyramid and ABCDEF is the base. > Altitude is the  segment from the vertex to the base (h) > Lateral faces are the six triangular faces (ex. VBC) > are all lateral edges. s h E F A D O C B

  7. 1) The base is a regular polygon. 2) All the lateral edges are congruent. 3) All the lateral faces are ≅isosceles ’s. 4) The height of a lateral face is the slant height of the pyramid (denoted s). 5) The altitude is the height. 6) The altitude meets the base at its center. Regular pyramid properties:

  8. Lateral Area (LA) of a Regular Pyramid: is the area of just the “sides” LA= ½Ps NC 27A: theorem P = Perimeter of the Bases= slant height

  9. Surface Area (SA) of a Regular Pyramid: is the total area of the “bottom” + all “sides” SA = B+LA NC 27B: theorem (½Ps) B = area of the Base (formula depends on shape) P =Perimeter of the Bases= slant height (area of all the “sides”)

  10. SA = Example 1:Find the lateral area & surface area. The base is a regular polygon. Answer in both exact form & to the nearest hundredth. LA= ½ ps P=8+8+8 P=24 LA= ½ (24)(12) LA=144cm² SA = B + LA 12cm 8 8cm  171.71cm²

  11. Example 2:Find the lateral area & surface area. Answer in both exact form & to the nearest hundredth. LA = ½ ps P =15+15+15+15 P =60 LA = ½ (60)(18) LA = 540in² SA = B + LA B = s² B = (15)² B = 225 SA = 225 + 540 SA = 765in² 18in 15 15 15 15in

  12. Cone vertex vertex Axis slant height • A cone has a vertex and a circular base. • The axis is the segment that joins the vertex to the center of the base. • If the axis is  to the base, then the cone is a right cone. Axis h Altitude or height r Right Cone Oblique Cone

  13. 1) The base is circular. 2) The altitude is the height. 3) The slant height (denoted s) is the distance between the vertex and a point on the base edge. 4) If the height is  to the base, then the cone is a right cone. 5) The altitude meets the base at its center. Right cone properties:

  14. Lateral Area (LA) of a Right Cone: is the area of just the “sides” LA = ½(2r)s or LA= rs NC 28A: theorem

  15. Surface Area (SA) of a Right Cone: is the total area of the “bottom” + all “sides” SA = r²+ LA NC 28B: theorem (rs) r= radius of the Bases= slant height

  16. Example 3:Find the lateral area and surface area of a right cone whose base radius is 8cm and slant height of 15cm. Answer in both exact form & to the nearest hundredth. TIP: Try drawing the figure first Answers: a) b)

  17. Example 4:Find the lateral area and surface area of the following: 4 6 s

  18. HW G1 #10 (Due wed 2/15) Page 738 {3–25 odd, 32–35} TIP: Use Pythagorean Theorem for {15 & 21} to find slant height & Write ALL answers in exact form too.COPY FIGURES !!!

  19. Example 5:Find the surface area of a hexagonal pyramid with a lateral edge of 13cm and a base edge of 10cm.

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