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A solid metal cylinder was dropped into a cylindrical glass
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Updated on: 16 May 2020, 17:18
Updated on: 16 May 2020, 17:18
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Question Stats:
83% (01:24) correct
16% (01:47) wrong based on 54 sessions
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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
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Re: A solid metal cylinder was dropped into a cylindrical glass
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15 May 2020, 11:56
15 May 2020, 11:56
Expert Reply
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Re: A solid metal cylinder was dropped into a cylindrical glass
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15 May 2020, 19:36
15 May 2020, 19:36
1
What does it means 200rr?
Re: A solid metal cylinder was dropped into a cylindrical glass
[#permalink]
16 May 2020, 17:19
16 May 2020, 17:19
Expert Reply
Fixed . it was \(\pi\)
many thanks.
Kudo
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many thanks.
Kudo
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Re: A solid metal cylinder was dropped into a cylindrical glass
[#permalink]
17 May 2020, 15:53
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
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
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Updated on: 08 Jul 2020, 00:59
Updated on: 08 Jul 2020, 00:59
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1
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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.
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.
Re: A solid metal cylinder was dropped into a cylindrical glass
[#permalink]
18 May 2020, 05:46
18 May 2020, 05:46
Expert Reply
Awesomeee
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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
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
_________________
Re: A solid metal cylinder was dropped into a cylindrical glass
[#permalink]
18 May 2020, 06:03
18 May 2020, 06:03
1
[quote="Carcass"]Awesomeee
Thank You Carcass
Thank You Carcass
Re: A solid metal cylinder was dropped into a cylindrical glass
[#permalink]
07 Jul 2020, 23:51
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
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
Re: A solid metal cylinder was dropped into a cylindrical glass
[#permalink]
Updated on: 08 Jul 2020, 07:00
Updated on: 08 Jul 2020, 07:00
2
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.
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
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Re: A solid metal cylinder was dropped into a cylindrical glass
[#permalink]
08 Jul 2020, 02:46
08 Jul 2020, 02:46
Expert Reply
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
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]
04 Aug 2020, 07:56
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.
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.
Re: A solid metal cylinder was dropped into a cylindrical glass
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21 Sep 2021, 18:23
21 Sep 2021, 18:23
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