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Updated on: 22 May 2014, 03:48
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.
Last edited by Bunuel on 22 May 2014, 03:48, edited 2 times in total.
RENAMED THE TOPIC.
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Difficulty:
65%
(hard)
Question Stats:
57% (02:25) correct
43%
(02:31)
wrong
based on 129
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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
Curved Surface Area, \(CSA = 2*pi*(R+r)*l\)
Total Surface Area, \(TSA = CSA + 2*pi*(R^2-r^2)\)
side view.PNG [ 4.72 KiB | Viewed 3342 times ]
front view.PNG [ 8.23 KiB | Viewed 3337 times ]
\(\frac{CSA}{TSA} = \frac{2*pi*(R+r)*l}{[2*pi*(R+r)*l + 2*pi*(R^2-r^2)]}\)
= \(\frac{l}{(l+R-r)}\)
=\(\frac{3}{(3+2-1)}\)
=\(\frac{3}{4}\)
(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 3342 times ]
Attachment:
front view.PNG [ 8.23 KiB | Viewed 3337 times ]
\(\frac{CSA}{TSA} = \frac{2*pi*(R+r)*l}{[2*pi*(R+r)*l + 2*pi*(R^2-r^2)]}\)
= \(\frac{l}{(l+R-r)}\)
=\(\frac{3}{(3+2-1)}\)
=\(\frac{3}{4}\)
21 May 2014, 12:10
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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
Curved Surface area = 18 * Pi
Total Surface Area = 24* Pi
Ratio = 18*pi/24*Pi = 3/4
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 3371 times ]
gmatcurved.jpg [ 47.12 KiB | Viewed 3371 times ]
Curved Surface area = 18 * Pi
Total Surface Area = 24* Pi
Ratio = 18*pi/24*Pi = 3/4
15 Feb 2015, 10:07
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kundankshrivastava
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!!!!
