12.3 SA of Pyramids &amp; Cones

# 12.3 SA of Pyramids &amp; Cones - 12.3 Surface Area of...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## 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.

Ask a homework question - tutors are online