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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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New post 12 Feb 2012, 22:04
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

49% (02:12) correct 51% (02:13) wrong based on 206 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

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)?

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Re: Surface area of a cylinder  [#permalink]

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

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New post 25 Feb 2018, 22:26
What does right circular cylinder mean ? I know how to solve the question but i have heard this term for the first time

Please explain

Thanks

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

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New post 25 Feb 2018, 23:42
ra5867 wrote:
What does right circular cylinder mean ? I know how to solve the question but i have heard this term for the first time

Please explain

Thanks

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A right circular cylinder is a cylinder with the circular bases and with the axis joining the two centers of the bases perpendicular to the planes of the two bases.

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right-cylinder.png [ 10.3 KiB | Viewed 16961 times ]

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

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New post 08 Jul 2019, 04:23
enigma123 wrote:
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
—> 2h + r = 2h^2

Insufficient

(2) h = 15/r – r
—> h + r = 15/r
—> r(h + r) = 15

Surface area = 2*pi*r(r + h) = 2*pi*15 = 30*pi

Sufficient

IMO Option B

Pls Hit kudos if you like the solution

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Re: A right circular cylinder has a radius r and a height h.   [#permalink] 08 Jul 2019, 04:23
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