McGraw-Hill Education GRE 2019

Thus to calculate the surface area of a cube, just calculate the area of one face and

multiply that by six (since the cube has six sides). The formula for the surface area

of a cube is

SAcube = 6e^2 , where e = the length of an edge

If the area of one face of a cube is 81, what is the surface area of the cube?

SOLUTION: Since all faces have the same area, the surface area of the cube =

81 × 6 = 486.

Volume of a Rectangular Solid and Cube

The volume of a rectangular solid refers to the amount of space within that shape.

Volume is measured in cubic units, such as 2 cubic meters or 3.7 cubic inches. To

calculate the volume of a rectangular solid, just multiply all the dimensions:

Vrectangular solid = l × w × h

The same rule applies to a cube. But since all the edges of a cube are equal, you just

need one side of the cube to calculate a cube’s volume:

Vcube = e^3

If the volume of a rectangular solid with a length of 4, a width of 2, and a

height of x equals the volume of a cube with an edge of 4, what is x?

A 1

B 2

C 4

D 8

E 16

SOLUTION: Since the volumes are equal,

4 × 2 × x = 4^3

8 x = 64

x = 8

The correct answer is D.

CHAPTER 13 ■ GEOMETRY 423

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