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hexagon

by finance » Sun Aug 07, 2011 9:50 am
The U.S. Defense Department has decided that the Pentagon is an obsolete building and that
it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a
building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye
cutout in the center (somewhat like the current one) that is 50 feet on a side. What will be the
volume of the new building in cubic feet?
A. 3,937,500 cubic feet
B. 15,750 cubic feet
C. 11,550 cubic feet
D. 15,750 cubic feet
E. 3,937,500 3 cubic feet
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by gmatboost » Sun Aug 07, 2011 10:29 pm
This will never be asked on the GMAT. The numbers are too big. Also, the question would have to state that the building and cutout are regular hexagons.

Anyway, to answer with a shortcut:
Remember the formula for area of an equilateral triangle: https://blog.gmatboost.com/2011/08/02/me ... -triangle/
x^2*root(3)/4

A regular hexagon is 6 equilateral triangles together. Try to draw this.
So, the formula for area is
6 * x^2*root(3)/4 = 3x^2*root(3)/2

So, use that, plug in 200 to find the base area
Then, plug in 50 to find the cutout area
Subtract to find the actual area
Multiply the result by 70 to find the volume
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