California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

What is the surface area of a three-dimensional object?

1. Sum of the volumes of the shapes

2. Sum of the lengths of the edges

3. Sum of the areas of all the faces

4. Product of the dimensions

The correct answer is: Sum of the areas of all the faces

The surface area of a three-dimensional object refers to the total area that covers the outside of the object. It is calculated by adding together the areas of all the individual faces or surfaces that make up the shape. This means that for any polyhedron or three-dimensional figure, finding the surface area involves determining the area of each face (which can be shapes like squares, rectangles, triangles, etc.) and then summing these areas to get the total surface area. Each of the other choices represents a different mathematical concept that does not accurately describe surface area. For example, the volume of a shape pertains to the space contained within, not the outer surface. The lengths of the edges correspond to the perimeter aspects of the shape rather than the area. The product of dimensions generally refers to calculating volume, not surface area. Thus, the correct definition of surface area is clearly the sum of the areas of all the faces.