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C. Surface Area of Composite Objects

Some structures are made of a combination of 3-D objects. These are called composite objects.

Composite object
formed by a combination of several 3-D objects

Often when a 3-D object is mentioned, it is implied that it is a right object. As such, an object may be called a cone, but is most likely a right cone, particularly when the context suggests so.

Much like finding the area of composite figures using basic shapes, begin to find the surface area of a composite object by identifying the basic objects that make up that composite object. Next, determine the surface area of each individual object, attending to areas of overlap and other necessary alterations to their formulas. Then, add or subtract some of these surface areas to determine the surface area of the given composite object.

Example 1

Consider the cabanas located at Lido Beach in Florida. The roof of each cabana is a cone and the walls are cylindrical. Determine a formula for the exposed surface area of one of the cabanas.

The base of the cone (a circle) and the top and base of the cylinder (two circles) do not contribute to the composite object's exposed surface area and thus must be eliminated from the composite object's surface area formula.