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A solid metal cylinder was dropped into a cylindrical glass

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Carcass
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A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   Updated on: 16 May 2020, 17:18
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A solid metal cylinder was dropped into a cylindrical glass originally holding \(200 \pi\) \(cm^3\) of water. If the metal cylinder has a radius of 3 centimeters and height of 7 centimeters, and is completely submerged in the water, by what percent did the water level in the glass rise? (Assume the metal is non-porous, so the resulting water and metal volume equals the original water volume plus the metal cylinder volume.)



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31.5

Originally posted by Carcass on 15 May 2020, 11:56.
Last edited by Carcass on 16 May 2020, 17:18, edited 1 time in total.
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   15 May 2020, 11:56
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Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   15 May 2020, 19:36
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What does it means 200rr?
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   16 May 2020, 17:19
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Fixed . it was \(\pi\)

many thanks.

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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   17 May 2020, 15:53
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volume of water in the glass cylinder = πr^2h1 = 200π; r^2 = 200/h1

volume of solid metal cylinder = π*3*3*7 = 63π
resulting water and metal volume in glass cylinder = 200π + 63π = 263π
if the water level reached up by h2 height, the filled volume in the glass cylinder = πr^2h2 = 263π;
h2 = 263/r^2 = (263/200)h1
percentage of water level rises in glass cylinder = (h2-h1)/h1 * 100

h2-h1)/h1 * 100
[(263/200)h1 - h1]/h1 * 100
63/200 * 100 = 31.5
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   Updated on: 08 Jul 2020, 00:59
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Volume of cylinder = π*r^2*h
Thus, 7*9*π = 63π
The water level in the glass increases from 200π by 200π+63π = 263π.
Percent increases = 263π-200π/200π * 100 = 63/200*100 = 31.5.

Originally posted by sukrut96 on 17 May 2020, 21:11.
Last edited by sukrut96 on 08 Jul 2020, 00:59, edited 1 time in total.
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   18 May 2020, 05:46
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Awesomeee


vndnjn wrote:
volume of water in the glass cylinder = πr^2h1 = 200π; r^2 = 200/h1

volume of solid metal cylinder = π*3*3*7 = 63π
resulting water and metal volume in glass cylinder = 200π + 63π = 263π
if the water level reached up by h2 height, the filled volume in the glass cylinder = πr^2h2 = 263π;
h2 = 263/r^2 = (263/200)h1
percentage of water level rises in glass cylinder = (h2-h1)/h1 * 100

h2-h1)/h1 * 100
[(263/200)h1 - h1]/h1 * 100
63/200 * 100 = 31.5
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   18 May 2020, 06:03
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[quote="Carcass"]Awesomeee

Thank You Carcass :-D
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   07 Jul 2020, 23:51
i have a doubt
is it possible any of these questions from the entire challenge are from the two free powerprep tests?
because i have'nt given them yet and would want to steer clear of them
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   Updated on: 08 Jul 2020, 07:00
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sukrut96 wrote:
Area of cylinder = π*r^2*h
Thus, 7*9*π = 63π
The water level in the glass increases from 200π by 200π+63π = 263π.
Percent increases = 263π-200π/200π * 100 = 63/200*100 = 31.5.


Nice explanation, the only error is π*r^2*h is the formula of Volume of cylinder and not the Area

Originally posted by Farina on 08 Jul 2020, 00:05.
Last edited by Farina on 08 Jul 2020, 07:00, edited 2 times in total.
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   08 Jul 2020, 02:46
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tanvi1998 wrote:
i have a doubt
is it possible any of these questions from the entire challenge are from the two free powerprep tests?
because i have'nt given them yet and would want to steer clear of them


No,

the source is mGRE 100%

All the questions from powerprep are here https://gre.myprepclub.com/forum/gre-power ... html#p6284

See also Free GRE Materials - Where to get it!

https://gre.myprepclub.com/forum/free-gmat ... tml#p53911

Regards
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   04 Aug 2020, 07:56
Yes the answer is 63/200 as mentioned by others.

Adding to that: the answer can be obtained by simply doing percentage change in volume

(263pi - 200pi)/200pi = 63/200

That is, the percentage change in volume is the percentage change in height.

Why is this the case?

B/c percentage change in volume is happening solely due to percentage change in the height, since the height of the water level is the only variable changing when the metal cylinder is added to the water.
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Re: A solid metal cylinder was dropped into a cylindrical glass [#permalink] New post   21 Sep 2021, 18:23
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