12.3 Surface Area of Pyramids and Cones

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Presentation transcript:

12.3 Surface Area of Pyramids and Cones GEOMETRY: Chapter 12 12.3 Surface Area of Pyramids and Cones

A pyramid is a polyhedron in which the base is a polygon and the lateral faces are triangles with a common vertex, called the vertex of the pyramid. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 810.

The intersection of two lateral faces is a lateral edge The intersection of two lateral faces is a lateral edge. The intersection of the base and a lateral face is a base edge. The height of the pyramid is the perpendicular distance between the base and the vertex. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 810.

A regular pyramid has a regular polygon for a base, and the segment joining the vertex and the center of the base is perpendicular to the base.

The lateral faces of a regular pyramid are congruent isosceles triangles. The slant height of a regular pyramid is the height of a lateral face of the regular pyramid.

Ex. 1 A regular square pyramid has a height of 12 ft and a base edge length of 10 ft. Find the area of each lateral face of the pyramid. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.

Ex. 1 A regular square pyramid has a height of 12 ft and a base edge length of 10 ft. Find the area of each lateral face of the pyramid. Answer: 65 ft2 Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.

The surface area S of a regular pyramid is S= B + ½ Pl, Theorem 12.4: Surface Area of a Regular Pyramid The surface area S of a regular pyramid is S= B + ½ Pl, where B is the area of the base, P is the perimeter of the bae, and l is the slant height. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.

Ex. 2. Find the surface area of a regular octagonal pyramid if the slant height is 18 ft. the apothem of the base is 15.7 ft, and the sides of the base are 13 ft. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.

Ex. 2. Find the surface area of a regular octagonal pyramid if the slant height is 18 ft. the apothem of the base is 15.7 ft, and the sides of the base are 13 ft. Answer: 1752.4 ft2 Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.

A cone has a circular base and vertex that is not in the same plane as the base. The radius of the base is the radius of the cone. The height is the perpendicular distance between the vertex and the base. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.

In a right cone, the segment joining the vertex and the center of the base is perpendicular to the base, and the slant height is the distance between the vertex and a point on the base edge. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.

Theorem 12.5: Surface Area of Right Cone The surface area of a right cone is Where B is the area of the base, C is the circumference of the base, r is the radius of the base, and l is the slant height. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.

What is the surface area of the right cone? Ex. 3 What is the surface area of the right cone? Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.

What is the surface area of the right cone? Ex. 3 What is the surface area of the right cone? Answer: 360 (pi) cm2 Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.

Ex. 4 A carpenter uses a weight in the shape of a right cone to identify vertical lines. The cone has a radius of 6.5 mm and a height of 13 mm. Find the approximate lateral area of the weight. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 813.

Ex. 4 A carpenter uses a weight in the shape of a right cone to identify vertical lines. The cone has a radius of 6.5 mm and a height of 13 mm. Find the approximate lateral area of the weight. Answer: 297 mm2 Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 813.

12.3, p. 814, #3-13 all, 15-23 odds (16 questions)