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.
I was confusing with the pipe thick and the pipe inner diameter.
Now, It makes sense.