Surface Area of Pyramids and Cones 10 5

Surface Area of Pyramids and Cones 10 -5 Surface Area of Pyramids and Cones Warm Up Lesson Presentation Lesson Quiz Holt. Mc. Dougal Geometry Holt

10 -5 Surface Area of Pyramids and Cones Objectives Learn and apply the formula for the surface area of a pyramid. Learn and apply the formula for the surface area of a cone. Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid. Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Example 1 A: Finding Lateral Area and Surface Area of Pyramids Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and slant height 25 cm. Round to the nearest tenth, if necessary. Lateral area of a regular pyramid P = 4(14) = 56 cm Surface area of a regular pyramid B = 142 = 196 cm 2 Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones The vertex of a cone is the point opposite the base. The axis of a cone is the segment with endpoints at the vertex and the center of the base. The axis of a right cone is perpendicular to the base. The axis of an oblique cone is not perpendicular to the base. Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones The slant height of a right cone is the distance from the vertex of a right cone to a point on the edge of the base. The altitude of a cone is a perpendicular segment from the vertex of the cone to the plane of the base. Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Example 2 A: Finding Lateral Area and Surface Area of Right Cones Find the lateral area and surface area of a right cone with radius 9 cm and slant height 5 cm. L = rℓ Lateral area of a cone = (9)(5) = 45 cm 2 Substitute 9 for r and 5 for ℓ. S = rℓ + r 2 Surface area of a cone = 45 + (9)2 = 126 cm 2 Substitute 5 for ℓ and 9 for r. Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Example 2 B: Finding Lateral Area and Surface Area of Right Cones Find the lateral area and surface area of the cone. Use the Pythagorean Theorem to find ℓ. L = rℓ Lateral area of a right cone = (8)(17) Substitute 8 for r and 17 for ℓ. 2 = 136 in S = rℓ + r 2 = 136 + (8)2 = 200 in 2 Holt Mc. Dougal Geometry Surface area of a cone Substitute 8 for r and 17 for ℓ.

10 -5 Surface Area of Pyramids and Cones Check It Out! Example 2 Find the lateral area and surface area of the right cone. Use the Pythagorean Theorem to find ℓ. ℓ L = rℓ Lateral area of a right cone = (8)(10) Substitute 8 for r and 10 for ℓ. 2 = 80 cm S = rℓ + r 2 = 80 + (8)2 = 144 cm 2 Holt Mc. Dougal Geometry Surface area of a cone Substitute 8 for r and 10 for ℓ.

10 -5 Surface Area of Pyramids and Cones Check It Out! Example 3 The base edge length and slant height of the regular square pyramid are both multiplied by. Describe the effect on the surface area. Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Check It Out! Example 3 Continued 8 ft 10 ft original dimensions: 1 S = 2 Pℓ + B = 585 cm 2 multiplied by two-thirds: S= 1 Pℓ 2 +B = 260 cm 2 By multiplying the dimensions by two-thirds, the surface area was multiplied by. Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Example 4: Finding Surface Area of Composite Three. Dimensional Figures Find the surface area of the composite figure. Left-hand cone: The lateral area of the cone is L = rl = (6)(12) = 72 in 2. Right-hand cone: Using the Pythagorean Theorem, l = 10 in. The lateral area of the cone is L = rl = (6)(10) = 60 in 2. Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Example 4 Continued Find the surface area of the composite figure. Composite figure: S = (left cone lateral area) + (right cone lateral area) = 60 in 2 + 72 in 2 = 132 in 2 Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Lesson Quiz: Part I Find the lateral area and surface area of each figure. Round to the nearest tenth, if necessary. 1. a regular square pyramid with base edge length 9 ft and slant height 12 ft L = 216 ft 2; S = 297 ft 2 Holt Mc. Dougal Geometry

10 -5 Surface Area of Pyramids and Cones Lesson Quiz: Part II 2. A right cone has radius 3 and slant height 5. The radius and slant height are both multiplied by. Describe the effect on the surface area. The surface area is multiplied by . 3. Find the surface area of the composite figure. Give your answer in terms of . S = 24 ft 2 Holt Mc. Dougal Geometry