首页
登录
职称英语
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
41
管理
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.
转载请注明原文地址:https://tihaiku.com/zcyy/3360491.html
相关试题推荐
Wehaveadesperateneed______practicestricteconomyineverydepartment.A、to
Theuniversity______pressuretocloseitsartdepartment.A、decidedB、madeC、resi
Atabouttwelveo’clock,themandecided_________toeathislunch.A、beingstoppe
Thisbuildingistallerthan________onearoundit.A、anyotherB、anotheroneC、an
Lastnighthesawtwodark________enterthebuilding,andthentherewastheexp
TheU.S.DefenseDepartmenthasdecidedthatthePentagonisanobsoletebuildin
Inordertoincreaserevenues,acell-phonecompanyhasdecidedtochangeitsfe
Anyannouncementauthorizedbytheheadofthedepartmentisimportant.However,
MannisCorporation’sarchivalrecordsarestoredinanobsoleteformatthatisa
Inseveralnineteenth-centurypaintingsthemarblebuildingsoftheAcropolisin
随机试题
It’snormaltothinkofaconversationastakingplacebetweenpeoplewhoar
太极拳(Taijiquan)是中华民族的宝贵财富,是东方文化的重要组成部分。作为中国古老的武术(martialarts)之一,其主要功能是武术攻防、锻炼
加强自我修养的途径是()。A.组织活动、委托任务 B.学习、座右铭、立志、自我
“由用药顺序确定最可疑致病药物.有意识地停用最可疑或引起相互作用的药物→根据停药
B
注意事项 1.申论考试与传统的作文考试不同,是分析驾驭材料的能力与表达能力并重
会员制期货交易所理事会会议应当于会议召开()日前通知全体理事。A.5 B
多动(注意缺陷)障碍的诊断要点是()。 (A)严重的注意力维持困难(B)常
施工图预算的编制方法主要有单价法和()两种。A:综合法 B:实物法 C:人工
在市场经济中,政府对运输服务实行征税,税收额由()承担。A:消费者 B:中间商
最新回复
(
0
)