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12 Feb 2012, 22:04
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
49% (02:09) correct
51%
(02:13)
wrong
based on 532
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A right circular cylinder has a radius r and a height h. What is the surface area of the cylinder?
(1) r = 2h – 2/h
(2) h = 15/r – r
(1) r = 2h – 2/h
(2) h = 15/r – r
Guys - any idea how the answer is B? Also can you please let me know when to take the surface area of cylinder as 2 pi*r*h and when to take it as 2*pi*r(r+h)?
13 Feb 2012, 00:41
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The answer has to be B.
Total Surface Area of Cylinder = \(2{\pi}r^2+2{\pi}rh\) (We have to find the surface area of the caps of the cylinder and then the sides)
\(2{\pi}r^2\) represents the area of the two caps
\(2{\pi}rh\) represents the area of the sides of the cylinder
To answer you specific question regarding when to use which formula, the first one i.e. \(2{\pi}rh\) is used when you are not accounting for the caps of the cylinder and the 2nd one i.e. \(=2{\pi}r^2+2{\pi}rh\) or as you put it \(=2{\pi}r*({r+h})\) is used when you are taking the caps in the surface area as well.
Statement 1: \(r=2h-\frac{2}{h}\). Just for the sake of understanding the question let's not deal with this right now.
Statement 2: \(h=\frac{15}{r}-r\)
So Area of Cylinder \(=2{\pi}r^2+2{\pi}rh\)
Substitute value of h:
So Area\(=2{\pi}r^2+2{\pi}r*(\frac{15}{r}-r)\)
So Area\(=2{\pi}r^2+2{\pi}r*(\frac{{15-r^2}}{r})\)
So Area\(=2{\pi}r^2+2{\pi}(15-r^2)\)
So Area\(=2{\pi}r^2+30{\pi}-2{\pi}r^2\)
So Area\(=30{\pi}\)
Hence B is sufficient.
Now if you use the same methodology with A you cannot end up with a reduced expression that just gives you a value. Hence A is not sufficient and B is.
Hope it helps..
Total Surface Area of Cylinder = \(2{\pi}r^2+2{\pi}rh\) (We have to find the surface area of the caps of the cylinder and then the sides)
\(2{\pi}r^2\) represents the area of the two caps
\(2{\pi}rh\) represents the area of the sides of the cylinder
To answer you specific question regarding when to use which formula, the first one i.e. \(2{\pi}rh\) is used when you are not accounting for the caps of the cylinder and the 2nd one i.e. \(=2{\pi}r^2+2{\pi}rh\) or as you put it \(=2{\pi}r*({r+h})\) is used when you are taking the caps in the surface area as well.
Statement 1: \(r=2h-\frac{2}{h}\). Just for the sake of understanding the question let's not deal with this right now.
Statement 2: \(h=\frac{15}{r}-r\)
So Area of Cylinder \(=2{\pi}r^2+2{\pi}rh\)
Substitute value of h:
So Area\(=2{\pi}r^2+2{\pi}r*(\frac{15}{r}-r)\)
So Area\(=2{\pi}r^2+2{\pi}r*(\frac{{15-r^2}}{r})\)
So Area\(=2{\pi}r^2+2{\pi}(15-r^2)\)
So Area\(=2{\pi}r^2+30{\pi}-2{\pi}r^2\)
So Area\(=30{\pi}\)
Hence B is sufficient.
Now if you use the same methodology with A you cannot end up with a reduced expression that just gives you a value. Hence A is not sufficient and B is.
Hope it helps..
General Discussion
16 Feb 2012, 05:54
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when it is asking for surface area of cylinder , we should take whole area ie area of two circles and curved surface area also and its 2pirsqr + 2pirh as mentioned by you........
take first equation we will get into complex calclutaion,
so immediatly go on second opton u will get h + r = 15/r subsitite that in the equaiton as mentioned by you 2pir(r+h) we will get total surface area is 30pi , will save one minute defintly
hope its clear.
take first equation we will get into complex calclutaion,
so immediatly go on second opton u will get h + r = 15/r subsitite that in the equaiton as mentioned by you 2pir(r+h) we will get total surface area is 30pi , will save one minute defintly
hope its clear.
