In silence look at the following images please

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

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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. ) 11

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Now, tell me what the concept is: Cones! (so smart again… I knew you could do it. ) 18

Mr. Owh Today is: Tuesday, February 13 th, 2007 Lesson 12. 3 – Surface Area of Pyramids & Cones • NC 27 A, 27 B, 28 A, 28 B Announcements: • Quiz for 12. 1 – 12. 3 is this Thursday (2/15) • You will need a calculator for this chapter 19

Lesson 12. 3 – Surface Areas of Pyramids & Cones • Today’s Objectives: Ø Find the surface area of a pyramid. Ø 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 20

Hexagonal Pyramid ABCDEF V s h E F A O D C B > 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. 21

Regular pyramid properties: 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. 22

NC 27 A: theorem Lateral Area (LA) of a Regular Pyramid: is the area of just the “sides” LA = ½Ps P = Perimeter of the Base s = slant height 23

NC 27 B: theorem Surface Area (SA) of a Regular Pyramid: is the total area of the “bottom” + all “sides” SA = B + LA (½Ps) B = area of the Base (formula depends on shape) P = Perimeter of the Base (area of all the “sides”) s = slant height 24

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=144 cm² 12 cm 8 SA = B + LA SA = 8 cm 171. 71 cm² 25

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 = 540 in² 18 in 15 SA = B + LA B = s² B = (15)² B = 225 SA = 225 + 540 SA = 765 in² 15 15 in 15 26

Cone vertex slant height vertex Axis h Altitude or height r Right Cone Oblique Cone Ø A cone has a vertex and a circular base. Ø The axis is the segment that joins the vertex to the center of the base. Ø If the axis is to the base, then the cone is a right cone. 27

Right cone properties: 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. 28

NC 28 A: theorem Lateral Area (LA) of a Right Cone: is the area of just the “sides” LA = ½(2 r)s or LA = rs 29

NC 28 B: theorem Surface Area (SA) of a Right Cone: is the total area of the “bottom” + all “sides” SA = r² + LA ( rs) r = radius of the Base s = slant height 30

Example 3: Find the lateral area and surface area of a right cone whose base radius is 8 cm and slant height of 15 cm. Answer in both exact form & to the nearest hundredth. TIP: Try drawing the figure first Answers: a) b) 31

Example 4: Find the lateral area and surface area of the following: 6 4 s 32

HW G 1 #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 !!! 33

Example 5: Find the surface area of a hexagonal pyramid with a lateral edge of 13 cm and a base edge of 10 cm. 34