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# A room of height 10 feet and equal length and width has a cylindrical

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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12 Sep 2018, 00:43
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Difficulty:

45% (medium)

Question Stats:

66% (01:42) correct 34% (02:06) wrong based on 66 sessions

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A room of height 10 feet and equal length and width has a cylindrical pillar exactly in the center, what is the volume of the room excluding the space occupied by the pillar?

(1) The farthest horizontal distance from any point in the room to the pillar is 10 feet.
(2) The area occupied by the base of the pillar is 4π feet.

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A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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12 Sep 2018, 05:11
Bunuel wrote:
A room of height 10 feet and equal length and width has a cylindrical pillar exactly in the center, what is the volume of the room excluding the space occupied by the pillar?

(1) The farthest horizontal distance from any point in the room to the pillar is 10 feet.
(2) The area occupied by the base of the pillar is 4π feet.

Question : Volume of cubical room = Volume of Cylinder $$= a^3 - πr^2h =$$?
Also, Height of the pillar = a

Statement 1: The farthest horizontal distance from any point in the room to the pillar is 10 feet

i.e. $$(1/2)*(a√2-2r) = 10$$

NOT SUFFICIENT

Statement 2: The area occupied by the base of the pillar is 4π feet

i.e. $$πr^2 = 4π$$
i.e. $$r = 2$$
btu a is still unknown hence
NOT SUFFICIENT

Combining the two statements
we can substitute $$r=2$$ in $$(1/2)*(a√2-2r) = 10$$ to calculate value of a hence

SUFFICIENT

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Posts: 903
Re: A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 10:14
GMATinsight wrote:
Bunuel wrote:
A room of height 10 feet and equal length and width has a cylindrical pillar exactly in the center, what is the volume of the room excluding the space occupied by the pillar?

(1) The farthest horizontal distance from any point in the room to the pillar is 10 feet.
(2) The area occupied by the base of the pillar is 4π feet.

Question : Volume of cubical room = Volume of Cylinder $$= a^3 - πr^2h =$$?
Also, Height of the pillar = a

Statement 1: The farthest horizontal distance from any point in the room to the pillar is 10 feet

i.e. $$(1/2)*(a√2-2r) = 10$$

NOT SUFFICIENT

Statement 2: The area occupied by the base of the pillar is 4π feet

i.e. $$πr^2 = 4π$$
i.e. $$r = 2$$
btu a is still unknown hence
NOT SUFFICIENT

Combining the two statements
we can substitute $$r=2$$ in $$(1/2)*(a√2-2r) = 10$$ to calculate value of a hence

SUFFICIENT

Dear GMATinsight,

Please can you explain statement 1 , what do we mean by "The farthest horizontal distance from any point in the room to the pillar is 10 feet."

Also how do we know that the room is a cube ? When the question says height 10 and equal length and width this can be interpreted two ways :
First: Height = 10 = Length = width
Second: A room has height 10 , whose length and width are equal.

Hope you can help, thank you.
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- Stne
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Joined: 02 Sep 2016
Posts: 9
A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 11:24
1
stne : here is what statement 1 says, visualize the cylinder in the center of the room. From Top view you can see a square with equal lengths(Say L) with a circle (with radius r) in the center.

Farthest horizontal distance will be from corner to the circumference of the circle:

HTH
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Joined: 27 May 2012
Posts: 903
A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 11:41
veekoul wrote:
stne : here is what statement 1 says, visualize the cylinder in the center of the room. From Top view you can see a square with equal lengths(Say L) with a circle (with radius r) in the center.

Farthest horizontal distance will be from corner to the circumference of the circle:

HTH

Wow veekoul,

First post towards me , I feel highly honored. On behalf of all here , let me welcome you to the Gmat club.
You have certainly cleared one aspect of my question. Thank you.
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- Stne
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Re: A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 11:52
stne - Thank you for the note !
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Re: A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 19:59
1
stne wrote:
GMATinsight wrote:
Bunuel wrote:
A room of height 10 feet and equal length and width has a cylindrical pillar exactly in the center, what is the volume of the room excluding the space occupied by the pillar?

(1) The farthest horizontal distance from any point in the room to the pillar is 10 feet.
(2) The area occupied by the base of the pillar is 4π feet.

Question : Volume of cubical room = Volume of Cylinder $$= a^3 - πr^2h =$$?
Also, Height of the pillar = a

Statement 1: The farthest horizontal distance from any point in the room to the pillar is 10 feet

i.e. $$(1/2)*(a√2-2r) = 10$$

NOT SUFFICIENT

Statement 2: The area occupied by the base of the pillar is 4π feet

i.e. $$πr^2 = 4π$$
i.e. $$r = 2$$
btu a is still unknown hence
NOT SUFFICIENT

Combining the two statements
we can substitute $$r=2$$ in $$(1/2)*(a√2-2r) = 10$$ to calculate value of a hence

SUFFICIENT

Dear GMATinsight,

Please can you explain statement 1 , what do we mean by "The farthest horizontal distance from any point in the room to the pillar is 10 feet."

Also how do we know that the room is a cube ? When the question says height 10 and equal length and width this can be interpreted two ways :
First: Height = 10 = Length = width
Second: A room has height 10 , whose length and width are equal.

Hope you can help, thank you.

stne

Farthest horizontal distance from pillar = distance between a corner of room and pillar = Half of the diagonal of the square on ground

We have not assumed room is a cube... Only the length and width are equal as given in question

First: Height = 10 = Length = width WRONG INTERPRETATION
Second: A room has height 10 , whose length and width are equal. RIGHT INTERPRETATION

I hope this helps!!!
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A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 21:17
Shouldnt it be E. Height is not specified ?
Can you pleaase help me imagine this one.

Thanks

chetan2u
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Re: A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 22:18
ShankSouljaBoi wrote:
Shouldnt it be E. Height is not specified ?
Can you pleaase help me imagine this one.

Thanks

ShankSouljaBoi Height is given as 10 feet in first line of question.

Quote:
A room of height 10 feetand equal length and width has a cylindrical pillar exactly in the center, what is the volume of the room excluding the space occupied by the pillar?

(1) The farthest horizontal distance from any point in the room to the pillar is 10 feet.
(2) The area occupied by the base of the pillar is 4π feet.

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Re: A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 22:31
Height of cylindrical pipe

Posted from my mobile device
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Re: A room of height 10 feet and equal length and width has a cylindrical  [#permalink]

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29 Oct 2018, 22:50
1
ShankSouljaBoi wrote:
Height of cylindrical pipe

Posted from my mobile device

As the question mentioned that it's a pillar and not a Pipe

I think it's evident that the pillar supports the ceiling and originates from ground level.

Isn't it???
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Re: A room of height 10 feet and equal length and width has a cylindrical   [#permalink] 29 Oct 2018, 22:50
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