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Name_____________________________________ Class____________________________ Date________________ Lesson 11-3 Surface Areas of Pyramids and Cones Lesson Objectives 1 Find the surface area of a pyramid 2 Find the surface area of a cone NAEP 2005 Strand: Measurement Topic: Measuring Physical Attributes Local Standards: ____________________________________ Theorem 11-3: Lateral and Surface Area of a Regular Pyramid The lateral area of a regular pyramid is half the product of the and the . L.A. B The surface area of a regular pyramid is the sum of the and the . Theorem 11-4: Lateral and Surface Area of a Cone The lateral area of a right cone is half the product of the and the . B L.A. 12 ? 2πr ? , or L.A. r The surface area of a right cone is the sum of the lateral area and the area of the base. S.A. A regular pyramid is The altitude of a pyramid or a cone is The height of a pyramid or a cone is edge Lateral face The slant height of a regular pyramid is Base The lateral area of a pyramid is edge Regular Pyramid The surface area of a pyramid is 212 Geometry Lesson 11-3 Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. S.A. All rights reserved. Vocabulary and Key Concepts. Name_____________________________________ Class____________________________ Date ________________ A right cone is The slant height of a cone is / h r The lateral area of a cone is All rights reserved. The surface area of a cone cone Examples. 1 Finding Surface Area of a Pyramid Find the surface area of a square pyramid with base edges 7.5 ft and slant height 12 ft. 12 ft © Pearson Education, Inc., publishing as Pearson Prentice Hall. 7.5 ft The perimeter p of the square base is 4 You are given find the lateral area. ft and you found that p L.A. 5 L.A. 5 12 ft, or ft. ft, so you can Use the formula for lateral area of a pyramid. ( )( ) L.A. 5 Substitute. Simplify. Find the area of the square base. Because the base is a square with side length 7.5 ft, B s2 S.A. 5 S.A. 5 2 1 . Use the formula for surface area of a pyramid. 1 S.A. 5 Substitute. Simplify. The surface area of the square pyramid is Daily Notetaking Guide ft2. Geometry Lesson 11-3 213 Name_____________________________________ Class____________________________ Date ________________ 2 Finding Lateral Area of a Cone Leandre uses paper cones to cover her plants in the early spring. The diameter of each cone is 1 ft, and its height is 1.5 ft. How much paper is in the cone? Round your answer to the nearest tenth. Use the formula L.A. to find the lateral area of the cone. ft. The cone’s diameter is 1 ft, so its radius r is 2 2 All rights reserved. The altitude of the cone, radius of the base, and slant height form a triangle. Use the to find the slant height . Find the lateral area. L.A. 5 Use the formula for lateral area of a cone. ( L.A. 5 p ) L.A. < Substitute for r and for . Use a calculator. The lateral area of the cone is about ft2. Quick Check. © Pearson Education, Inc., publishing as Pearson Prentice Hall. 1. Find the surface area of a square pyramid with base edges 5 m and slant height 3 m. 2. Find the lateral area of a cone with radius 15 in. and height 20 in. to the nearest square inch. 214 Geometry Lesson 11-3 Daily Notetaking Guide