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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. The shape of a tepee suggests a circular cone. Cones have the following characteristics:

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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. The shape of a tepee suggests a circular cone. Cones have the following characteristics: • The base of a cone is a circle and the vertex is the point at the top of the cone where the sides meet, in this case it is point V. • The axis is 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 perpendicular to the base is called the altitude of the cone. V altitude axis base

  4. Right and Oblique Cones • A cone with an axis that is also an altitude is called a right cone. Otherwise, it is called an oblique cone. On a right cone the segment from the vertex to the edge of the circular base is called the slant height, l. The measure of the altitude is the height. Oblique Cone Right Cone altitude l axis Altitude and axis Slant height h r

  5. Example 2 Hunter has a lamp that has an altitude of 12 inches and a diameter of 18 inches. Find the lateral area of the lamp shade. Write an equation and solve for l. l2 =122 + 92 Pythagorean Theorem l2=225 Simplify l = 15 Take square root of each side. Next, use the formula for lateral area of a right circular cone. L = 3.14(r)(l) Lateral area of a cone. = 3.14(9)(15) r=9, l = 15 = 423.9 Use a calculator l 12in. 18 in.

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