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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Thu Sep 30, 2010 2:48 pm

A spherical ball, when immersed in a cylinder of base radius 14cm, raises the level of water in the cylinder by 4cm. Find the radius of the ball in cm
A) cuberoot 588
B) cuberoot 147/2
C) Sqrt 94/7
D) cuberoot 147
E) Cannot be determined
how to sold this guys?
i know this problem was posted in this forum before but i am not comfortable with the solution....

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Source: Beat The GMAT — Problem Solving | Thu Sep 30, 2010 2:48 pm

limestone: Master | Next Rank: 500 Posts; Posts: 307; Joined: Sun Jul 11, 2010 7:52 pmFollowed by: 1 member; Thanked: 36 times; GMAT Score:640

by limestone » Thu Sep 30, 2010 6:53 pm

The rising in the level of water in the cylinder is due to the increase in volume that is equal to the volume of the spherical ball.

Then the volume increased (the increase volume is in the shape of a cylinder):
V(I) = r^2*Pi*Height = 14^2*Pi*4 = 784*Pi

The volume of the sperical ball (which cause the increase in volume of the original cylinder):
V(S) = 4/3*Pi*r^3

V(I) = V(S), then:
4/3*Pi*r^3 = 784*Pi
r^3 = 784* 3/4 = 588
Then r = cuberoot (588)

Pick A.

"There is nothing either good or bad - but thinking makes it so" - Shakespeare.

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neerajkumar1_1: Master | Next Rank: 500 Posts; Posts: 270; Joined: Wed Apr 07, 2010 9:00 amFollowed by: 2 members; Thanked: 24 times

by neerajkumar1_1 » Thu Sep 30, 2010 6:54 pm

diebeatsthegmat wrote:A spherical ball, when immersed in a cylinder of base radius 14cm, raises the level of water in the cylinder by 4cm. Find the radius of the ball in cm
A) cuberoot 588
B) cuberoot 147/2
C) Sqrt 94/7
D) cuberoot 147
E) Cannot be determined
how to sold this guys?
i know this problem was posted in this forum before but i am not comfortable with the solution....

There is one simple physics attribute in this problem
i.e the amount of fluid displaced is equal to the volume of the object...

Now...

when a sphere is added in a tank, the height changes by 4

so lets consider the original volume of the liquid in the cylinder to be = V = pi * R^2 * h

where R= 14 given and h is the height of fluid before we immersed the object

Let V` = volume of water in the cylinder after the object is immersed = pi * R^2 * (h+4)

so now the volume of the sphere = V`- V = pi * R^2 * 4

Also volume of a sphere = 4/3 * pi * r^3, where r is the radius of the sphere...

Therefore
4/3 * pi * r^3 = pi * R^2 * (h+4)

=> r = cuberoot of (588)

IMO A

Hope this helps...

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Thu Sep 30, 2010 8:00 pm

limestone wrote:The rising in the level of water in the cylinder is due to the increase in volume that is equal to the volume of the spherical ball.

Then the volume increased (the increase volume is in the shape of a cylinder):
V(I) = r^2*Pi*Height = 14^2*Pi*4 = 784*Pi

The volume of the sperical ball (which cause the increase in volume of the original cylinder):
V(S) = 4/3*Pi*r^3

V(I) = V(S), then:
4/3*Pi*r^3 = 784*Pi
r^3 = 784* 3/4 = 588
Then r = cuberoot (588)

Pick A.

why do we know this ? " The rising in the level of water in the cylinder is due to the increase in volume that is equal to the volume of the spherical ball. "

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limestone: Master | Next Rank: 500 Posts; Posts: 307; Joined: Sun Jul 11, 2010 7:52 pmFollowed by: 1 member; Thanked: 36 times; GMAT Score:640

by limestone » Thu Sep 30, 2010 10:47 pm

Hi,

This is a little out side the scope. It's about physic.

When you submerge something into the water, that thing will take the room of some water. As water cannot be compressed, then that room must be equal to the volume of the object you have just submerged ( of course, that object must not interact with or absorb water).

This method is used to calculate the volume of complex objects. For instance,people submerge a ring into a cup of water that has a parimeter on its side, then see how much the column of water has risen. Using the parimeter printed on the cup, people can figure out the volume of risen water (as in the above case, I use base's area * increased height to find the increased volume). And that risen volume is also the volume of the ring.

"There is nothing either good or bad - but thinking makes it so" - Shakespeare.

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Thu Sep 30, 2010 11:55 pm

diebeatsthegmat wrote: why do we know this ? " The rising in the level of water in the cylinder is due to the increase in volume that is equal to the volume of the spherical ball. "

It is the Archimede's principle. More to do with physics. This has a funny history. Archimedes+EUREKA. read this snippet from wikipedia:

"This exclamation is most famously attributed to the ancient Greek scholar Archimedes; he reportedly proclaimed "Eureka!" when he stepped into a bath and noticed that the water level rose - he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. This meant that the volume of irregular objects could be calculated with precision, a previously intractable problem. He is said to have been so eager to share his realisation that he leapt out of his bathtub and ran through the streets of Syracuse naked."

(In case, you are not comfortable with this problem, I suggest you to Ignore this question.)

"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sun Oct 03, 2010 7:51 am

limestone wrote:Hi,

This is a little out side the scope. It's about physic.

When you submerge something into the water, that thing will take the room of some water. As water cannot be compressed, then that room must be equal to the volume of the object you have just submerged ( of course, that object must not interact with or absorb water).

This method is used to calculate the volume of complex objects. For instance,people submerge a ring into a cup of water that has a parimeter on its side, then see how much the column of water has risen. Using the parimeter printed on the cup, people can figure out the volume of risen water (as in the above case, I use base's area * increased height to find the increased volume). And that risen volume is also the volume of the ring.

physic??? i am hella bad at physic... always get D lol

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sun Oct 03, 2010 7:56 am

kvcpk wrote:
diebeatsthegmat wrote: why do we know this ? " The rising in the level of water in the cylinder is due to the increase in volume that is equal to the volume of the spherical ball. "
It is the Archimede's principle. More to do with physics. This has a funny history. Archimedes+EUREKA. read this snippet from wikipedia:

"This exclamation is most famously attributed to the ancient Greek scholar Archimedes; he reportedly proclaimed "Eureka!" when he stepped into a bath and noticed that the water level rose - he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. This meant that the volume of irregular objects could be calculated with precision, a previously intractable problem. He is said to have been so eager to share his realisation that he leapt out of his bathtub and ran through the streets of Syracuse naked."

(In case, you are not comfortable with this problem, I suggest you to Ignore this question.)

i know the story of loving to be nude after finding a principle of Archimedes....
i dont understand much about physic but i will consider this a kind of rule in solving this sort of problem,,, i dont think they will test us physic in math section.
thank you both limestone and kvcpk

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