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An iron pipe used to transmit water is 3 m long and 1 m thic

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An iron pipe used to transmit water is 3 m long and 1 m thic [#permalink]

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New post 21 May 2014, 10:10
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An iron pipe used to transmit water is 3 m long and 1 m thick. Its outer diameter is 4 m. What is the ratio of its Curved Surface Area to its Total Surface Area?

(A) \(\frac{1}{4}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{3}{4}\)
(E) \(\frac{7}{8}\)


Source: Original Question


[Reveal] Spoiler:

SOLUTION



Curved Surface Area, \(CSA = 2*pi*(R+r)*l\)
Total Surface Area, \(TSA = CSA + 2*pi*(R^2-r^2)\)

Attachment:
side view.PNG
side view.PNG [ 4.72 KiB | Viewed 1462 times ]
Attachment:
front view.PNG
front view.PNG [ 8.23 KiB | Viewed 1462 times ]


\(\frac{CSA}{TSA} = \frac{2*pi*(R+r)*l}{[2*pi*(R+r)*l + 2*pi*(R^2-r^2)]}\)
= \(\frac{l}{(l+R-r)}\)
=\(\frac{3}{(3+2-1)}\)
=\(\frac{3}{4}\)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 May 2014, 02:48, edited 2 times in total.
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Re: Practice Question- Solid Geometry [#permalink]

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New post 21 May 2014, 11:10
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Length of pipe = 3 m
Outer Dia = 4 m => outer radius => 2 m
Inner Dia = 2-1 = 1 m

Curved area of outer surface = 2*pi* 2 * 3 =12*Pi
Curved area of inner surface = 2*pi*1*3 = 6*pi
Total curved surface area = 12Pi +6 Pi = 18 Pi
Total Surface Area = Total curved surface area + 2*Pi*(2^2 - 1^2)
= 18 Pi + 6 Pi = 24 Pi
Attachment:
File comment: ratio of areas
gmatcurved.jpg
gmatcurved.jpg [ 47.12 KiB | Viewed 1442 times ]


Curved Surface area = 18 * Pi
Total Surface Area = 24* Pi

Ratio = 18*pi/24*Pi = 3/4
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Re: An iron pipe used to transmit water is 3 m long and 1 m thic [#permalink]

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New post 15 Feb 2015, 09:07
kundankshrivastava wrote:
Length of pipe = 3 m
Outer Dia = 4 m => outer radius => 2 m
Inner Dia = 2-1 = 1 m

Curved area of outer surface = 2*pi* 2 * 3 =12*Pi
Curved area of inner surface = 2*pi*1*3 = 6*pi
Total curved surface area = 12Pi +6 Pi = 18 Pi
Total Surface Area = Total curved surface area + 2*Pi*(2^2 - 1^2)
= 18 Pi + 6 Pi = 24 Pi
Attachment:
gmatcurved.jpg


Curved Surface area = 18 * Pi
Total Surface Area = 24* Pi

Ratio = 18*pi/24*Pi = 3/4



Hi,

I do not understand if inner diameter is equal to 1 why the calculation of the total surface aera is not :

Total Surface Area = Total curved surface area + 2*Pi*(2^2 - (1/2)^2)?

Thanx in advance for your explanation!!!!
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Re: An iron pipe used to transmit water is 3 m long and 1 m thic [#permalink]

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New post 15 Feb 2015, 22:37
Millaeva wrote:
kundankshrivastava wrote:
Length of pipe = 3 m
Outer Dia = 4 m => outer radius => 2 m
Inner Dia = 2-1 = 1 m

Curved area of outer surface = 2*pi* 2 * 3 =12*Pi
Curved area of inner surface = 2*pi*1*3 = 6*pi
Total curved surface area = 12Pi +6 Pi = 18 Pi
Total Surface Area = Total curved surface area + 2*Pi*(2^2 - 1^2)
= 18 Pi + 6 Pi = 24 Pi
Attachment:
gmatcurved.jpg


Curved Surface area = 18 * Pi
Total Surface Area = 24* Pi

Ratio = 18*pi/24*Pi = 3/4



Hi,

I do not understand if inner diameter is equal to 1 why the calculation of the total surface aera is not :

Total Surface Area = Total curved surface area + 2*Pi*(2^2 - (1/2)^2)?

Thanx in advance for your explanation!!!!


Inner diameter is actually 2 giving you that inner radius is 1.

Note that the outer diameter is 4. Remove the thickness of the pipe (1 m) from each side to get inner diameter = 4 - 2 = 2 m. So inner radius is 1 m.

Also, note that if I had 30 secs to review the question and guess, I would have guessed 3/4 and moved on. The reason for this:

The total surface area of the pipe will be predominantly the curved surface area outside and inside. Only at the extremities do you have some extra surface area (area of outside circle - area of inside circle) which will be added to curved surface area to give you total surface area. Hence, ratio of curved to total cannot be 1/4, 1/3 or 1/2. Now note that the length of the pipe is only 3 m and its outer diameter is actually 4 m giving us a thick, short pipe with quite a bit of surface area at the extremes. Hence, I would guess that it should be 3/4 and not 7/8.
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Re: An iron pipe used to transmit water is 3 m long and 1 m thic [#permalink]

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New post 16 Feb 2015, 01:37
VeritasPrepKarishma wrote:
Millaeva wrote:
kundankshrivastava wrote:
Length of pipe = 3 m
Outer Dia = 4 m => outer radius => 2 m
Inner Dia = 2-1 = 1 m

Curved area of outer surface = 2*pi* 2 * 3 =12*Pi
Curved area of inner surface = 2*pi*1*3 = 6*pi
Total curved surface area = 12Pi +6 Pi = 18 Pi
Total Surface Area = Total curved surface area + 2*Pi*(2^2 - 1^2)
= 18 Pi + 6 Pi = 24 Pi
Attachment:
gmatcurved.jpg


Curved Surface area = 18 * Pi
Total Surface Area = 24* Pi

Ratio = 18*pi/24*Pi = 3/4



Hi,

I do not understand if inner diameter is equal to 1 why the calculation of the total surface aera is not :

Total Surface Area = Total curved surface area + 2*Pi*(2^2 - (1/2)^2)?

Thanx in advance for your explanation!!!!


Inner diameter is actually 2 giving you that inner radius is 1.

Note that the outer diameter is 4. Remove the thickness of the pipe (1 m) from each side to get inner diameter = 4 - 2 = 2 m. So inner radius is 1 m.

Also, note that if I had 30 secs to review the question and guess, I would have guessed 3/4 and moved on. The reason for this:

The total surface area of the pipe will be predominantly the curved surface area outside and inside. Only at the extremities do you have some extra surface area (area of outside circle - area of inside circle) which will be added to curved surface area to give you total surface area. Hence, ratio of curved to total cannot be 1/4, 1/3 or 1/2. Now note that the length of the pipe is only 3 m and its outer diameter is actually 4 m giving us a thick, short pipe with quite a bit of surface area at the extremes. Hence, I would guess that it should be 3/4 and not 7/8.



Hi,

This is my own mistake :-)
I was confusing with the pipe thick and the pipe inner diameter.
Now, It makes sense.

Thank you for this additionnal explanation!
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Re: An iron pipe used to transmit water is 3 m long and 1 m thic [#permalink]

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Re: An iron pipe used to transmit water is 3 m long and 1 m thic   [#permalink] 12 Aug 2017, 06:05
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