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

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Presentation on theme: "10-5 Surface Area of Pyramids and Cones Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz."— Presentation transcript:

1 10-5 Surface Area of Pyramids and Cones Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2 Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = c = 15, a = 9 3. b = 40, c = a = 5, b = 5 5. a = 4, c = 8 c = 25 b = 12 a = 9

3 Learn and apply the formula for the surface area of a pyramid and cone. Objectives

4 The vertex of a pyramid is the point opposite the base of the pyramid. The base of a regular pyramid is a regular polygon, and the lateral faces are congruent isosceles triangles. The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base.

5 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.

6 Lateral Area of a regular pyramid with perimeter, P and slant height l is _________ L = ½ P l Surface Area of a regular pyramid with lateral area L and base area B is ________________________ S = L + B or S = ½ P l + B

7 Example 1A: 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 = 14 2 = 196 cm 2

8 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.

9 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. Lateral Area of a right cone with radius, r and slant height l is _______ L =  r l Surface Area of a right cone with lateral area L and base area B is _______________________ S = L + B or S =  r l +  r 2

10 Example 2A: 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.

11 Example 2B: 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 = r ℓ = (8)(17) = 136 in 2 Lateral area of a right cone Substitute 8 for r and 17 for ℓ. S = r ℓ + r 2 Surface area of a cone = 136 + (8) 2 = 200 in 2 Substitute 8 for r and 17 for ℓ.

12 Find the lateral area and surface area of the right cone. Use the Pythagorean Theorem to find ℓ. L = r ℓ = (8)(10) = 80 cm 2 Lateral area of a right cone Substitute 8 for r and 10 for ℓ. S = r ℓ + r 2 Surface area of a cone = 80 + (8) 2 = 144 cm 2 Substitute 8 for r and 10 for ℓ. ℓ Example 2C: Finding Lateral Area and Surface Area of Right Cones

13 The base edge length and slant height of the regular square pyramid are both multiplied by. Describe the effect on the surface area. Example 3A: Exploring Effects of Changing Dimensions

14 Example 3A Continued original dimensions:multiplied by two-thirds: By multiplying the dimensions by two-thirds, the surface area was multiplied by. 8 ft 10 ft S = Pℓ + B 1212 = 260 cm 2 S = Pℓ + B 1212 = 585 cm 2


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