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

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Attachment:

#GREpracticequestion In the rectangular solid depicted above , AB = 6.JPG [ 17.4 KiB | Viewed 5895 times ]

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

Re: 3D figure geometry
[#permalink]
03 Feb 2019, 03:44

6

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.

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]
03 Feb 2019, 12:08

Expert Reply

Please post a question like this under the sub-forum: select one or more answer choices.

It is NOT a quantitative comparison question.

Regards

_________________

It is NOT a quantitative comparison question.

Regards

_________________

Re: 3D figure geometry
[#permalink]
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

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

Re: In the rectangular solid depicted above , AB = 6
[#permalink]
14 Jun 2020, 06:37

Well couldnt understand this

_________________

_________________

Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!!

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

Expert Reply

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.

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.

_________________

Re: 3D figure geometry
[#permalink]
22 Jul 2020, 06:50

SusieSushi wrote:

[

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

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

Hi

Nothing is stopping you to choose number, please make sure the number selection falls in criteria if mentioned in the question

and choosing decimal/ fraction will only consume time

_________________

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Re: In the rectangular solid depicted above , AB = 6
[#permalink]
22 Jul 2020, 06:54

2

Farina wrote:

Well couldnt understand this

Hi,

Let me know what you have not understood?

As a brief, we got a rectangular solid, which is divided to form a triangle.

Now, how can we get the volume of shaded area?

simple, First we need the total volume of the rectangle

second, we need the volume of the triangle

Shaded volume = Total volume of the rectangle - volume of the triangle

I hope this help

_________________

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Re: In the rectangular solid depicted above , AB = 6
[#permalink]
01 Mar 2021, 17:55

1

This is how I solved it. We know that AB = 6 so AE + EB = 6. We also know that 2<EB<AE which means that 2<EB<3 because if EB was 3 then AE would also have to be 3 which doesn't work as EB must be smaller than AE. This also means that 3<AE<4 because if AE = 4 or greater, than EG=2 or smaller which can't be the case. I then thought of the unshaded area as half of a rectangular prism with the height=AE, W= 5 and L=8. We know that the volume of a rectangular prism is HxLxW. I plugged in 3 and 4 for AE to get the upper and lower limits for the volume. V= 3x8x5 --> 120 and V= 4x8x5 ---> 160. I then divided these by two because the unshaded portion is only half of a rectangular prism. 120/2 = 60 and 160/2=80. Through this we know that the upper unshaded section has a volume between 60 and 80. We can than find what the volume would be in the shaded area by finding the volume of the entire rectangular prism and subtracting the upper and lower limits of the unshaded area. Volume of prism = 6x8x5 --->240 240 - 60 = 180, 240-80= 160. Therefore, the volume of the shaded area must be between 160 and 180. The only answer that falls within this range is D (170).

Re: In the rectangular solid depicted above , AB = 6
[#permalink]
22 Sep 2023, 08:57

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