Difference between revisions of "2007 iTest Problems/Problem 27"
(Created page with "== Problem == The face diagonal of a cube has length <math>4</math>. Find the value of n given that <math>n\sqrt2</math> is the <math>\textit{volume}</math> of the cube. == Sol...") |
Rockmanex3 (talk | contribs) (Solution to Problem 27) |
||
Line 3: | Line 3: | ||
The face diagonal of a cube has length <math>4</math>. Find the value of n given that <math>n\sqrt2</math> is the <math>\textit{volume}</math> of the cube. | The face diagonal of a cube has length <math>4</math>. Find the value of n given that <math>n\sqrt2</math> is the <math>\textit{volume}</math> of the cube. | ||
− | == Solution == | + | ==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 <math>4</math>, then by using 45-45-90 triangles, the side length of the cube is <math>2 \sqrt{2}</math>. Thus, the volume of the cube is <math>(2 \sqrt{2})^3 = 16 \sqrt{2}</math>, so <math>n = \boxed{16}</math>. | ||
+ | |||
+ | ==See Also== | ||
+ | {{iTest box|year=2007|num-b=26|num-a=28}} | ||
+ | |||
+ | [[Category:Introductory Geometry Problems]] |
Latest revision as of 19:15, 10 June 2018
Problem
The face diagonal of a cube has length . Find the value of n given that
is the
of the cube.
Solution
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 |