10-5 Surface Area of Pyramids & Cones

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Presentation transcript:

10-5 Surface Area of Pyramids & Cones Geometry

Pyramid Polyhedron in which the base is a polygon and the lateral faces are triangles with a common vertex.

Regular pyramid Has a regular polygon for a base and its height meets the base at its center. Slant height of a reg. pyramid is the altitude of any lateral face.

Lateral Area of a regular pyramid Where l =slant height

S.A. of a Regular Pyramid S.A. = B= Area of the base P= Perimeter of the base l = slant height S.A. = B + L.A.

Ex. 1 Find the lateral area & surface area of the regular pyramid shown. ℓ= 16 in. 10 in

Cones Has a circular base and a vertex that is not in the same plane as the base. Right Cone – the ht meets the base at its center and slant ht is the distance between the vertex and a point on the base edge.

Lateral Area of a Right Cone

S.A. of a Right Cone S.A. = r = radius of base l = slant height

Ex. 2 Find the lateral area & surface area of the right cone shown. Give your answers in terms of l h = 15 in. r= 8 in Ex. Ex. 3

Ex. 3 Find the surface area of each composite figure r=6 in, h= 8 in, l=12 in 8 in.

Assignment

Ex. 2 A regular pentagonal pyramid has a base with sides of length 18 inches, an apothem of about 12.4 inches and a slant height of 24 inches. Find the surface area of the pyramid.

Ex. 3 Finding the slant ht #21 pg. 739