## GMAT Quantitative Review

## 3.0 Math Review

### 3.3 Geometry

### 9. Rectangular Solids and Cylinders

A *rectangular solid* is a three-dimensional figure formed by 6 rectangular surfaces, as shown below. Each rectangular surface is a *face*. Each solid or dotted line segment is an *edge*, and each point at which the edges meet is a *vertex*. A rectangular solid has 6 faces, 12 edges, and 8 vertices. Opposite faces are parallel rectangles that have the same dimensions. A rectangular solid in which all edges are of equal length is a *cube*.

The *surface area* of a rectangular solid is equal to the sum of the areas of all the faces. The *volum*e is equal to

.

In the rectangular solid above, the dimensions are 3, 4, and 8. The surface area is equal to . The volume is equal to .

The figure above is a right circular *cylinder*. The two bases are circles of the same size with centers *O* and *P*, respectively, and altitude (height) is perpendicular to the bases. The surface area of a right circular cylinder with a base of radius *r* and height *h* is equal to (the sum of the areas of the two bases plus the area of the curved surface).

The volume of a cylinder is equal to , that is,

.

In the cylinder above, the surface area is equal to

,

and the volume is equal to

.