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In the rectangular solid depicted above , AB = 6

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In the rectangular solid depicted above , AB = 6 [#permalink] New post 02 Feb 2019, 20:18
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Question Stats:

21% (02:09) correct 78% (02:28) wrong based on 52 sessions
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In the rectangular solid depicted above , AB = 6, BC = 8, CD = 5, and AE > EB > 2.

Which of the following could be possible values for the volume of the shaded area?

a) 60

b) 70

c) 150

d) 170

e) 180

f) 240
[Reveal] Spoiler: OA
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Re: 3D figure geometry [#permalink] New post 03 Feb 2019, 03:44
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SKH121 wrote:
In the rectangular solid depicted above (please look at attached figure), AB = 6, BC = 8, CD = 5, and AE > EB > 2. Which of the following could be possible
values for the volume of the shaded area? Answer = D
a) 60
b) 70
c) 150
d) 170
e) 180
f) 240

Please if anyone can solve this question.



Explanation::

Volume of the rectangular solid = 6 × 8 × 5 = 240.

Now the length of 2 < BE < 3 < AE < 4 because if AE is 4 then EB = 2 that violates the condition AE > EB > 2

Now we need the volume of the triangular space (Not Shaded) and there is a need to take 2 condition i.e when AE =3 and AE = 4

Volume of the triangle = Area * Height

When AE = 3 then the area of the \(\triangle\) = 12 , Volume = 12 * 5 = 60


When AE = 4 then the area of the \(\triangle\) = 16 , Volume = 16 * 5 = 80

Hence The shaded area’s volume falls between 240 – 80 = 160 and 240 – 60 = 180 i.e. Option D 170
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Re: In the rectangular solid depicted above , AB = 6 [#permalink] New post 03 Feb 2019, 12:08
Expert's post
Please post a question like this under the sub-forum: select one or more answer choices.

It is NOT a quantitative comparison question.

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Re: 3D figure geometry [#permalink] New post 13 Nov 2019, 14:53
[

When faced with a definition such as AE > EB > 2, is there any strategy in terms of what numbers we should choose? I plugged in 2.5 because I thought both AE = 3 and AE = 4 would fail the condition
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Re: In the rectangular solid depicted above , AB = 6 [#permalink] New post 14 Jun 2020, 06:37
Well couldnt understand this :(
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Re: In the rectangular solid depicted above , AB = 6 [#permalink] New post 14 Jun 2020, 09:13
Expert's post
OE


Find the volume of the entire box, which equals 6 × 8 × 5 = 240. Solve for the volume of the three-dimensional triangular shape on top and subtract it from the total volume to find the volume of the shaded part. The triangular shape has known dimensions of 8 by 5. The third dimension ranges based on the length of BC, with 3 < BC < 4 because BC has to be bigger than AB. Therefore, the triangular shape’s volume falls between one-half of 8 × 5 × 3 = 60 and one-half of 8 × 5 × 4 = 80. The shaded area’s volume falls between 240 − 80 = 160 and 240 − 60 = 180. Only choice (D) works.

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Re: In the rectangular solid depicted above , AB = 6   [#permalink] 14 Jun 2020, 09:13
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In the rectangular solid depicted above , AB = 6

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