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 volume 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

.