Difference between revisions of "1981 AHSME Problems/Problem 9"
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In the adjoining figure, <math>PQ</math> is a diagonal of the cube. If <math>PQ</math> has length <math>a</math>, then the surface area of the cube is | In the adjoining figure, <math>PQ</math> is a diagonal of the cube. If <math>PQ</math> has length <math>a</math>, then the surface area of the cube is | ||
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==See also== | ==See also== | ||
| − | {{AHSME box|year=1981|num-b= | + | {{AHSME box|year=1981|num-b=8|num-a=10}} |
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 13:42, 28 June 2025
Problem 9
In the adjoining figure, 
is a diagonal of the cube. If has length 
, then the surface area of the cube is
![[asy] import three; unitsize(1cm); size(200); currentprojection=orthographic(1/3,-1,1/2); draw((0,0,0)--(1,0,0)--(1,1,0)--(0,1,0)--cycle,black); draw((0,0,0)--(0,0,1),black); draw((0,1,0)--(0,1,1),black); draw((1,1,0)--(1,1,1),black); draw((1,0,0)--(1,0,1),black); draw((0,0,1)--(1,0,1)--(1,1,1)--(0,1,1)--cycle,black); draw((0,0,0)--(1,1,1),black); label("$P$",(0, 0, 0),NW); label("$Q$",(1, 1, 1),NE); [/asy]](http://latex.artofproblemsolving.com/9/d/9/9d9bfa9dd8764fa193435c4a769e67e0f0635f6b.png)
Solution
Because the space diagonal of a cube with side length 
is 
the side length of the cube in this problem is 
The surface area of the cube is therefore 
which is answer choice 
See also
| 1981 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
