2007 iTest Problems/Problem 27
Problem
The face diagonal of a cube has length 
. Find the value of n given that 
is the 
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]](http://latex.artofproblemsolving.com/2/b/e/2bec0076aa5c1e65a414f42b2e9c44fedb6c2115.png)
If the length of the face diagonal of the cube is , then by using 45-45-90 triangles, the side length of the cube is 
. Thus, the volume of the cube is 
, so 
.
See Also
| 2007 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 26 |
Followed by: Problem 28 | |
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