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Notes 46

Notes 46. Surface Area of Pyramids and Cones. Vocabulary. Regular pyramid- a pyramid whose base is a regular polygon, and the faces are congruent isosceles triangles. S lant height of a pyramid- the distance from the vertex to the midpoint of an edge of the base.

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Notes 46

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  1. Notes 46 Surface Area of Pyramids and Cones

  2. Vocabulary Regular pyramid- a pyramid whose base is a regular polygon, and the faces are congruent isosceles triangles. Slant height of a pyramid- the distance from the vertex to the midpoint of an edge of the base. Slant height of a cone- the distance from the vertex to a point on the edge of the base.

  3. The base of a regular pyramid is a regular polygon, and the faces are congruent isosceles triangles. The diagram shows a square pyramid. The blue dashed line labeledl is the slant height of the pyramid, the distance from the vertex to the midpoint of an edge of the base.

  4. 1 2 S = lw + Pl 1 2 S = (9 • 9) + (36)(10)‏ Additional Example 1A: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B = lw Substitute. P = 4(9) = 36 S = 81 + 180 Add. S = 261 m2 The surface area is 261 square meters.

  5. 1 2 1 2 S = bh + Pl 1 2 S = (12)(10.38) + (36)(6)‏ Additional Example 1B: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B= ½bh. 1 2 S = 62.28 + 108 S = 170.28 The surface area is 170.28 m2.

  6. Check It Out: Example 1A Find the surface area ofeachpyramid.

  7. Check It Out: Example 1B Find the surface area of the pyramid

  8. The diagram shows a cone and its net. The blue dashed line is the slant height of the cone, the distance from the vertex to a point on the edge of the base.

  9. Additional Example 2: Finding the Surface Area of a Cone Find the surface area of the cone. Use 3.14 for . S = r2 + rl Use the formula. S ≈ (3.14)(32) + (3.14)(3)(10)‏ Substitute. S ≈ 28.26 + 94.2 Multiply. S ≈ 122.46 Add. The surface area is about 122.46 square centimeters.

  10. Check It Out: Example 2A Find the surface area of the cone. Use 3.14 for .

  11. Check It Out: Example 2B The dimensions of the cone from Exercise 2a quadrupled. Find the surface area of the cone. Use 3.14 for .

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