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

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Intern
Joined: 19 May 2014
Posts: 30
An iron pipe used to transmit water is 3 m long and 1 m thic  [#permalink]

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Updated on: 22 May 2014, 03:48
1
5
00:00

Difficulty:

85% (hard)

Question Stats:

53% (02:28) correct 47% (02:33) wrong based on 120 sessions

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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

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 [ 4.72 KiB | Viewed 1787 times ]
Attachment:

front view.PNG [ 8.23 KiB | Viewed 1787 times ]

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

Originally posted by JapinderKaur on 21 May 2014, 11:10.
Last edited by Bunuel on 22 May 2014, 03:48, edited 2 times in total.
RENAMED THE TOPIC.
Intern
Joined: 14 May 2014
Posts: 40
Re: Practice Question- Solid Geometry  [#permalink]

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21 May 2014, 12:10
2
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 [ 47.12 KiB | Viewed 1768 times ]

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

Ratio = 18*pi/24*Pi = 3/4
Intern
Joined: 29 Jan 2015
Posts: 3
Re: An iron pipe used to transmit water is 3 m long and 1 m thic  [#permalink]

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15 Feb 2015, 10:07
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)?

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: An iron pipe used to transmit water is 3 m long and 1 m thic  [#permalink]

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15 Feb 2015, 23:37
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)?

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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Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 29 Jan 2015
Posts: 3
Re: An iron pipe used to transmit water is 3 m long and 1 m thic  [#permalink]

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16 Feb 2015, 02:37
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)?

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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12 Aug 2017, 07:05
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Re: An iron pipe used to transmit water is 3 m long and 1 m thic   [#permalink] 12 Aug 2017, 07:05
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