11.3 and 11.5: Pyramids and Cones. Pyramids Pyramid – A 3-D figure with one face (the base) that is any polygon and the other faces (the lateral faces)

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Presentation transcript:

11.3 and 11.5: Pyramids and Cones

Pyramids Pyramid – A 3-D figure with one face (the base) that is any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex. Regular Pyramid – Base is a regular polygon. Slant Height ( l ) – The length of an altitude of a lateral face of the pyramid. How are the height and slant height related to the edge of the base of a pyramid???

Surface Area of Pyramids THEOREM 11.3 – Surface Area of Regular Pyramid The surface area of a regular pyramid is the sum of the lateral area and the area of the base.

Surface Area of Pyramid The Great Pyramid of Giza, Egypt has a height of 481 ft. Each edge of its square base is about 756 ft. Find the area of the surface of the pyramid.

Cones Cone – A 3-D figure with a circular base and a curved lateral surface How are the radius, height, and slant height related???

Surface Area of Cones THEOREM 11.4 – Surface Area of Cone The surface area of a cone is the sum of the lateral area and the area of the base. Find the surface area of the following cone.

Surface Area of Cones The radius of the base of a cone is 5 m. If the height of the cone is 12 m, find the surface area in terms of π.

Volume of Pyramids THEOREM 11.8 – Volume of Pyramid The volume of a pyramid is one third the product of the area of a base and the height of the pyramid. The Pyramid arena in Memphis, TN has a base of area 300,000 ft 2. Its height is 321 ft. What is the volume of the pyramid?

Volume of Pyramids Find the volume of the following pyramid.

Volume of Cones THEOREM 11.9 – Volume of Cone The volume of a cone is one third the product of the area of the base and the height of the cone. Find the volume of the following cone in terms of π.

Volume of Cones Find the volume of the following cone in terms of π.

11.3 and 11.5: Pyramids and Cones Homework: p.620 #1-13 odd, 18 p.634 #7-14, 18