12.3 SA of Pyramids & Cones

12.3 SA of Pyramids & Cones - 12.3 Surface Area of...

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Unformatted text preview: 12.3 Surface Area of Pyramids & Cones Pyramids p. 735 Pyramid Pyramid • Defn. – a polyhedron with a polygon base & polyhedron lateral faces (all ∆ s) that share a common s) vertex. vertex. • Altitude (height - h) - ⊥ distance from vertex to base. to • Base Edge – the edge of the base. • Regular Pyramid – base is a regular polygon & the height intersects the base at its center. center. • Slant Height ( l ) – (only in reg. pyramids!) altitude of a lateral face. altitude Pyramid (continued) Pyramid Regular pyramid Vertex Oblique pyramid Slant height sq ua re Base edge Base on g ta en p Lateral faces are all the triangles! Ex: If the height of the regular pyramid is Ex If 12 cm and a base edge is 10 cm, what is the length of the slant height? the 12 5 l 12 h l 10 Use Pythagorean Theorem! 122 + 52 = l 2 10 144 + 25 = l 2 144 169 = l 2 169 13 cm = l 13 Thm 12.4 – SA of a regular pyramid Thm S = B + ½ Pl B – area of the base, P – perimeter of area the base, & l – slant height What about lateral area? * remember, it’s everything BUT the remember, base area base SO, LA = ½ Pl Ex: Find the lateral & surface areas of the Ex Find regular pyramid given that a base edge is 4 ft and the slant height is 9 ft. and LA = ½ Pl LA = ½ (4*6)(9) LA = 108 ft2 S = B + ½ Pl B = ½ Pa 120 B = ½ (4*6)(2ð3 ) B =24ð 3 S = 24ð 3 + 108 4 2ð S = 149.57 ft2 3 60 o o 2 Cone Cone • Defn. – like a pyramid with a circular like base. base. Oblique Cone h • Right Cone – height meets the base at its center. its Thm 12.5 – SA of a right Cone Thm S = B + ½ Cl Or S = π r2 + ½ (2π r)l So, S = π r2 + π rl So, What about lateral area? Again, it’s everything BUT the base area, so LA = π rl LA Ex: Find the lateral & surface areas of the right cone. of 6 in l = 10 10 LA = π rl LA LA = π (6)(10) LA LA = 60π in2 S = π r2 + π rl S = π (62) + 60π S = 36π + 60π S = 96π in2 How do you find the slant How Use Pythag. Thm! height? height? 82 + 62 = l 2 10 = l 10 8 in Assignment Assignment ...
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This note was uploaded on 02/12/2011 for the course MTG 3212 taught by Professor Jackson during the Spring '11 term at University of Florida.

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