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

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A right circular cylinder has a radius r and a height h. [#permalink]

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12 Feb 2012, 22:04
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46% (02:31) correct 54% (01:22) wrong based on 181 sessions

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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

[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]

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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..
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Re: A right circular cylinder has a radius r and a height h. [#permalink]

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16 Feb 2012, 05:54
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]

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19 Oct 2013, 18:31
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Re: A right circular cylinder has a radius r and a height h. [#permalink]

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31 Aug 2015, 23:12
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Re: A right circular cylinder has a radius r and a height h. [#permalink]

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22 Sep 2016, 02:40
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Re: A right circular cylinder has a radius r and a height h. [#permalink]

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24 Feb 2017, 03:34
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Prompt analysis
Surface area = 2*pi*r(r+h)

Superset
The value will be a positive real number

Translation
In order to find the answer, we need:
1# exact value of r and h.
2# Value of r^2 and rh
3# two equation 2 variables(r and h) to calculate r and h

Statement analysis
St 1: replace r or h with the term in h or r respectively and you will still be left with an expression in one variable
St 2: If you replace h with given expression, after solving, you will be left with 30pi, which is constant. ANSWER

Option B
Re: A right circular cylinder has a radius r and a height h.   [#permalink] 24 Feb 2017, 03:34
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# A right circular cylinder has a radius r and a height h.

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