All SAT II Math I Resources
Example Questions
Example Question #2 : Other 3 Dimensional Geometry
If a cube has a surface area of then what is the the length of its longest diagonal?
Possible Answers:
Correct answer:
Explanation:
The longest diagonal of a cube transverses the interior of the figure:
This distance is defined by the super pythagorean theorem :
where ,
, and
are the length, width, and height. Because the figure is a cube, all three are the same measure, and each is the side of the cube.
We can use the given surface area to find the length of the side:
We can use this value for the side to plug into the super pythagorean theorem
Which can be simplified to
All SAT II Math I Resources
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