## 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 6*a ^{2},* 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

*(a*that cover it.

^{2})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 *a*^{3}.