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A right circular cylinder has a radius r and a height h.

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Director
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A right circular cylinder has a radius r and a height h. [#permalink] New post 12 Feb 2012, 21:04
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

41% (02:42) correct 59% (01:21) wrong based on 66 sessions
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

[Reveal] Spoiler:
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)?
[Reveal] Spoiler: OA

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Re: Surface area of a cylinder [#permalink] New post 12 Feb 2012, 23:41
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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..
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Re: A right circular cylinder has a radius r and a height h. [#permalink] New post 16 Feb 2012, 04:54
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.
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Re: A right circular cylinder has a radius r and a height h. [#permalink] New post 19 Oct 2013, 17:31
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Re: A right circular cylinder has a radius r and a height h.   [#permalink] 19 Oct 2013, 17:31
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