10.1.2 Surface Area of Pyramids and Cones (continued) Example 2 Finding Lateral Area and Surface Area of Right Cones
The lateral area of a right cone is equal to πrl , where l is the slant height. This is equivalent to one half the base circumference times the slant height. The surface area of a right cone is equal to the lateral area plus the base area. The base area is equal to the area of a circle with radius r .
The lateral and surface area of a right cone are determined in this example. The figure is given as a right cone with radius 4 meters and slant height 7 meters. To calculate the lateral surface area, substitute the known values into the formula for lateral surface area. The lateral surface area is 28 π m 2 . To calculate the surface area of the cone, substitute the known values into the formula for surface area. The area of the base is πr 2 . The surface area is 44 π m 2 . The lateral and surface area of a right cone are determined in this example. The figure is given as a right cone with radius 6 feet and altitude 8 feet. To calculate the lateral surface area, substitute the known values into the formula for lateral surface area. Use the Pythagorean Theorem to calculate the slant length, or recognize that it is the hypotenuse of a 6, 8, 10 Pythagorean triple. The lateral surface area is 60 π ft 2 . To calculate the surface area of the cone, substitute the known values into the formula for surface area. The area of the base is πr 2 . The surface area is 96 π ft 2 .
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