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Surface Areas of Cones

Surface Areas of Cones. Find the lateral areas of cones. Find surface areas of cones. A cone-shaped teepee in a Shoshone camp, South Pass, Wyoming 1870. LATERAL AREAS OF CONES. Cones have the following characteristics: The base is a circle and the vertex is the point V .

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Surface Areas of Cones

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  1. Surface Areas of Cones • Find the lateral areas of cones. • Find surface areas of cones. A cone-shaped teepee in a Shoshone camp, South Pass, Wyoming 1870

  2. LATERAL AREAS OF CONES • Cones have the following characteristics: • The base is a circle and the vertex is the point V. • The axis is the segment whose endpoints are the vertex and the center of the base. • The altitude is the segment from the vertex perpendicular to the base of the cone.

  3. LATERAL AREAS OF CONES The axis is also an altitude Slant height Axis Altitude l Oblique Cone Right Cone

  4. LATERAL AREAS OF CONES We can use the net for the cone to derive the formula for the lateral area. r l l r

  5. LATERAL AREAS OF CONES • The lateral region of the cone is a sector of a circle with radius l • The arc length of the sector is the same as the circumference of the base, or 2r. • The circumference of the circle containing the sector is 2l • The area of the sector is proportional to the area of the circle. l r r l

  6. LATERAL AREAS OF CONES • The area of the sector is proportional to the area of the circle. l area of sector = measure of arc area of circle = circumference of circle area of sector = 2r 2l2 = 2l (l2)(2r) area of sector = 2l area of sector = rl r r l

  7. Key ConceptLateral Area of a Cone If a right circular cone has a lateral of L square units, a slant height of l units, and the radius of the base is r units, then L = rl l r

  8. Example 1Lateral Area of a Cone LAMPS Diego has a conical lamp shade with an altitude of 6 inches and a diameter of 12 inches. Find the lateral area of the lamp shade. 6 in. 12 in.

  9. SURFACE AREAS OF CONES To find the surface area of a cone, add the area of the base to the lateral area.

  10. Key ConceptSurface Area of a Cone If a right circular cone has a surface area of T square units, a slant height of l units, and the radius of the base is r units, then T = rl + r2 l r

  11. Example 2Surface Area of a Cone 13.6 cm 4.7 cm.

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