Geometry and Trigonometry
Measurements and Transformations
How are the surface area and volume of a three-dimensional geometric figure calculated?
The surface area (often abbreviated S.A.) of a three-dimensional geometric figure is the total surfaces of the solid; it actually has units of distance or length squared. For example, the surface area of a cube is 6a2, in which a is the length of the sides. To translate, a cube has sides of equal lengths (a); the area of a cube is the sum of the areas of the six squares (a2) that cover it.
For more “diverse” figures, the surface area is actually equal to the lateral area plus the area of each base. For example, the surface area of a prism or cylinder is the lateral area plus the area of each base. (Because the bases for a prism or cylinder are congruent, this is often expressed as twice the area of the base.) The surface area of a pyramid or cone is the lateral area plus the area of the single base.
The volume of a three-dimensional geometric figure is the total amount of space the object occupies; volumes of such objects have units of length cubed. For example, the volume of a box (also called a rectangular parallelepiped) is length times width times height, or l × w × h; the volume of a cube is all the sides a cubed, or a3.