11-3 Surface Areas of Pyramids and Cones

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Presentation transcript:

11-3 Surface Areas of Pyramids and Cones Course: Geometry Pre-IB Quarter: 3rd Objective: Find the surface area of a pyramid. Find the surface area of a cone. SSS: MA.912.G.7.5; MA.912.G.7.7

Pyramids A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at the vertex. A pyramid is named by its base. The altitude, or height, of a pyramid is the perpendicular distance from the vertex to the base. A regular pyramid is one whose base is a regular polygon (lateral faces = isos. triangles). The slant height l is the length of the altitude of a lateral face.

Areas of Pyramids The lateral area of a pyramid is the sum of the areas of the congruent lateral faces. LA = ½Pl The surface area is the sum of the lateral area and the area of the base. SA = LA + B

Finding the Surface Area of a Pyramid What is the surface area of the hexagonal pyramid?

 A square pyramid has base edges of 5 m and a slant height of 3 m  A square pyramid has base edges of 5 m and a slant height of 3 m. What is the surface area?

 What is the surface area of the hexagonal pyramid?

Cones A cone is a solid that has a circular base and a vertex not in the same plane as the base. In a right cone, the height is a perpendicular segment from the vertex to the center of the base. The slant height is the distance from the vertex to a point on the edge of the base. Assume cones area right cones unless stated or pictured otherwise.

Areas of Cones The lateral area is half the circumference of the base times the slant height. LA = πrl The surface area of a cone is the sum of the lateral area and the area of the base. SA = LA + B

Finding the Surface Area of a Cone What is the surface area of the cone in terms of π?

 The radius of the base of a cone is 16 m. Its slant height is 28 m  The radius of the base of a cone is 16 m. Its slant height is 28 m. What is the surface area in terms of π?