McGraw-Hill Education GRE 2019

Surface Area of a Rectangular Solid and a Cube

The following figure is a rectangular solid:

Width

Edge

Length

Height

Face

The edge of a rectangular solid refers to any line that joins two vertices, and the

face of a rectangular solid refers to any of the rectangles formed by four edges. All

rectangular solids have six faces, and opposite faces have the same dimensions.

The surface area of any three-dimensional shape refers to the total area

covered by the shape’s surface.

It may seem tedious to calculate surface area of a rectangular solid, since you

would presumably need to calculate the area of each face. But remember that

opposite faces have the same dimensions. So instead of calculating the area of each

face, just calculate the area of each unique face and double that.

The formula for calculating surface area of a rectangular solid is therefore:

SArectangular solid = 2lw + 2lh + 2wh

What is the surface area of a rectangular solid with dimensions 3 × 4 × 5?

SOLUTION: Use the preceding formula. Let l = 3, w = 4, and h = 5. Substitute:

2(3)(4) + 2(3)(5) + 2(4)(5) = 94.

A cube is a type of rectangular solid in which all edges are equal. Since all edges

of a cube are equal, all faces will have an equal area.

Cube

422 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 422 12/05/17 12:05 pm