2. 职称英语
  3. The U.S. Defense Department has decided that the Pentagon is an obsolete buildin

The U.S. Defense Department has decided that the Pentagon is an obsolete buildin

游客2024-01-14  27
问题 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?
选项 A、3,937,500 cubic feet
B、15,750 cubic feet
C、 
D、 
E、 
答案 E
解析 This is very definitely a multi-step problem. First, you need to recognize that we’re dealing with nothing more than an oddly-shaped cylinder: the base is a regular polygon, so by dividing it into a number of manageable pieces, we can calculate its area. However, before we do that, we’ll need to figure out how to treat that hole in the middle of the six-sided doughnut. The easiest thing to do is to think about it as "negative area"--to calculate its area, and then subtract that area from the area of the larger, filled-in shape to find the area of the region around it. The following diagram below shows the three steps:
   Next, we’ll need to calculate the areas of those two different triangles. If you happen to remember the formula for the area of an equilateral triangle, great; skip to that step. If not, you’ll need to derive it. That’s not that hard: using the diagram that follows, you can divide the equilateral triangle into two right triangles, each with height h, hypotenuse a (there go those shifting variable names again), and base a/2. Since we don’t know what h is, it would be nice to state that in terms of a as well. We’ll do that first, by relying on the Pythagorean Theorem:

   Step 4: Calculate the area of the triangle
   The area of the entire equilateral triangle is just twice the area of the right "half triangle" on either side:

   Six of these form the whole of the large (outer) hexagon, so that area is:

   Six of the smaller triangles form the whole of the hole in the middle. We’ll need a different variable for these, since we’re talking about a different a at this point. We can define these as the outer ao and inner ai sides:
   The area of the Hexagon (minus the bull’s eye)=
   Then, the height is a uniform 70 feet all around, so finding the volume is just a matter of multiplying through by that height:
   Of course, that doesn’t look much like the answer choices, so we’ll need to substitute the values for the variables:
   If you looked over the answer choices, you will know that  is an acceptable component of your answer; the thrust of this question is geometry, so the GMAT would not make you calculate a square root as part of the problem. The volume corresponds with answer choice E.
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