2007 iTest Problems/Problem 27

Problem

The face diagonal of a cube has length $4$ . Find the value of n given that $n\sqrt2$ is the $\textit{volume}$ of the cube.

Solution

$[asy] draw((0,0)--(10,0)--(10,10)--(0,10)--(0,0)); draw((10,0)--(0,10)); label("$4$",(5,5),NE); label("$s$",(5,0),S); label("$s$",(0,5),W); [/asy]$

If the length of the face diagonal of the cube is $4$ , then by using 45-45-90 triangles, the side length of the cube is $2 \sqrt{2}$ . Thus, the volume of the cube is $(2 \sqrt{2})^3 = 16 \sqrt{2}$ , so $n = \boxed{16}$ .

2007 iTest (Problems, Answer Key)
Preceded by: Problem 26	Followed by: Problem 28
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2007 iTest Problems/Problem 27

Problem

Solution

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