10.2.2 Surface Area of Pyramids and Cones (continued)
Example 3 Exploring Effects of Changing Dimensions
The effect on surface area of a proportional increase in the dimensions of a right cone are examined in this example. The dimensions of the cone are given as a radius of 2 feet and a slant height of 7 feet. To find the surface area of the right cone, substitute the given values into the formula. The surface area of the cone is 18 π ft 2 . In the new cone, the radius and slant height are doubled and have the values 4 ft and 14 ft. To find the surface area of the new cone, substitute these values into the formula. The larger cone has surface area 72 π ft 2 . The larger cone has a surface area that is 2 2 = 4 times the surface area of the original cone, which is the square of the factor used to increase the dimensions.
Example 4 Finding Surface Area of Composite Three-Dimensional Figures
The surface area of a composite solid is calculated in this example. The solid is given as a cube with a square pyramid on top of it. The length of an edge of the cube is given as 5 cm and the slant height of the pyramid is given as 8 cm. First, calculate the lateral area of the pyramid. The length of the edge of the cube is the same as the length of the edge of the pyramid base, so the perimeter of the base is 4(5) = 20 cm. Substitute the slant height and base perimeter into the formula for lateral area. The lateral area of the pyramid is 80 cm 2 . Second, calculate the area of five sides of the cube, since the sixth is not on the surface of the composite object. The surface area of one side is 5 2 = 25 cm 2 , so the surface area of five sides is 125 cm 2 . The total area of the object is 125 + 80 = 205 cm 2 .
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