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Surface Area Formulas for Pyramids and Cones: Explained and Applied

Learn how to justify and apply formulas for the surface area of pyramids and cones. Understand concepts like regular pyramid, slant height, and congruent faces through examples and diagrams. Master calculations for surface area with step-by-step explanations and additional practice problems.

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Surface Area Formulas for Pyramids and Cones: Explained and Applied

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Presentation Transcript

  1. Lesson Presentation

  2. Sunshine State Standards MA.7.G.2.1 Justify and apply formulas for surface area..of…pyramids…and cones. Also MA.7.G.2.2

  3. Vocabulary regular pyramid slant height of a pyramid slant height of a cone

  4. 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 labeled l is the slant height of the pyramid, the distance from the vertex to the midpoint of an edge of the base.

  5. 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.

  6. 1 2 1 2 S = bh + Pl 1 2 1 2 S = (7)(6) + (21)(8) 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. Substitute. P = 3(7) = 21 S = 21 + 84 Add. S = 105 in2 The surface area is 105 square inches.

  7. 5 m 1 2 S = lw + Pl 3 m 3 m 1 2 S = (3 • 3) + (12)(5) Check It Out: Example 1A Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B= lw. Substitute. P = 4(3) = 12 S = 9 + 30 Add. S = 39 m2 The surface area is 39 square meters.

  8. 4 in. 1 2 1 2 S = bh + Pl 1 2 1 2 S = (4)(3) + (12)(6) 6 in. 4 in. 4 in. 3 in. Check It Out: Example 1B Find the surface area of the pyramid 1 2 S = B + Pl Use the formula. B= ½bh. Substitute. P = 3(4) = 12 S = 6 + 36 Add. S = 42 in2 The surface area is 42 square inches.

  9. 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.

  10. 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.

  11. Check It Out: Example 2 Find the surface area of the cone. Use 3.14 for . S = r2 + rl Use the formula. S ≈ (3.14)(42) + (3.14)(4)(10) Substitute. S ≈ 50.24 + 125.6 Multiply. S ≈ 175.84 Add. The surface area is about 175.84 square centimeters.

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