GMAT Quantitative Review

3.0 Math Review

3.3 Geometry

9. Rectangular Solids and Cylinders

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

image.

image

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

image

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) image 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 image (the sum of the areas of the two bases plus the area of the curved surface).

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

image.

image

In the cylinder above, the surface area is equal to

image,

and the volume is equal to

image.