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12-6 Surface Area of Cones

12-6 Surface Area of Cones. Objectives. Find lateral areas of cones. Find surface areas of cones. Cones. The base is a circle and the vertex is point V The axis is the segment with endpoints that are the vertex and the center of the base.

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12-6 Surface Area of Cones

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  1. 12-6 Surface Area of Cones

  2. Objectives • Find lateral areas of cones. • Find surface areas of cones.

  3. Cones • The base is a circle and the vertex is point V • The axisis the segment with endpoints that are the vertex and the center of the base. • The segment that has the vertex as one endpoint and is ⊥ to the base is called the altitude of the cone. V l Slant Height r Axis and Altitude Right Cone

  4. V Axis l Altitude X Oblique Cone

  5. Lateral Area of Cones V l r l r

  6. Lateral Area of Cones V Lateral Area= slant height x πx radius or L=πrl l r l r

  7. Example 1 Find the lateral area of the cone. 12cm 4cm

  8. Example 1 Find the lateral area of the cone. L= πrl L= π(4)(12) L=150.8 Lateral area= 150.8cm2 12cm 4cm

  9. Total Surface Area V l r

  10. Total Surface Area V T= πrl + πr2 l r

  11. Example 2 Find the surface area of the cone. 8 m 6 m

  12. Example 2 Find the surface area of the cone. T= πrl + πr2 Use Pythagorean theorem to find l. T= π(6)(10) + π62 T= 301.6 Surface Area = 301.6 m2 8 m 6 m 10 m

  13. Example 3 Johnny has an ice cream cone that has a lateral area of 28 in and a slant height of 6 In. Find the diameter of his ice cream cone.

  14. Example 3 Johnny has an ice cream cone that has a lateral area of 28 in and a slant height of 6 In. Find the diameter of his ice cream cone. L= πrl 28= πr(6) r ≈1.5 d ≈3 Diameter ≈ 3 inches

  15. Assignment Page 668 #7-24, 30-32

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