McGraw-Hill Education GRE 2019

Diagonal of a Rectangular Solid

The diagonal of a rectangular solid is the straight line distance from one vertex to

the opposite vertex.

To determine the diagonal of a rectangular solid, use the following formula:

diagonalrectangular solid = √l^2 + w^2 + h^2

If a rectangular solid has dimensions of 5, 5, and 10, what is the greatest

straight-line distance from one vertex to another vertex?

A 10

B 20

C 25

D 5√ 2

E 5√ 6

SOLUTION: Use the formula: Let l = 5, w = 5, and h = 10. The diagonal =

√5^2 + 5^2 + 10^2 = √ 150 = 5√ 6. The correct answer is E.

The diagonal of a cube = e√3.

Cylinders

A cylinder is rectangular solid whose base is a circle.

Height

Base

To determine the volume of a cylinder, multiply the area of the base by the height.

In the case of a cylinder, the area of the base is πr^2 since the base is a circle. The

formula for the volume of a cylinder is

Vcylinder = πr^2 h

424 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 424 23/01/18 11:14 AM