A solid cylinder with radius 3 inches sits in a cylindrical

Question

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A solid cylinder with radius 3 inches sits in a cylindrical container containing water. The cylindrical container has radius 4 inches, and the water is 6/π inches deep. If the solid cylinder is removed from the container, what will be the depth of the water (in inches)?

A) \(\frac{2}{3π}\)

B) \(\frac{1}{π}\)

C) \(\frac{3}{2π}\)

D) \(\frac{2}{π}\)

E) \(\frac{3}{π}\)

* Kudos for all correct solutions

A)  \frac{2}{3π}

B)  \frac{9}{4π}

C)  \frac{7}{3π}

D)  \frac{21}{8π}

E)  \frac{3}{π}

* Kudos for all correct solutions

EDIT: I changed the answer choices after I was alerted to a mistake I made.

rohit8865 · Answer

total volume with cylender inserted - volume of only cylender = volume of water with new height
16π*6/π - 9π*6/π = 16π*H
thus H= 21/8π...........

not getting answer!!!!!!!!!

can anyone explian!!!!!!!!

goodie · Answer

Same problem

Volume of water: volume of water tank - volume of inserted cylinder = 16π*6/π - 9π*6/π = 96 - 54 = 42

Now for this volume we need to find new height with given radius:

16π*h = 42

h=42/16π = 21/8π

Does not agree with option choices

mbah191 · Answer

I also got 21/8π, which does not agree with any of the answer choices.

BrentGMATPrepNow · Answer

Argh!!!! I solved that question TWICE before posting it and, each time I subtracted 96 - 54, I got 32 (instead of 42) :oops:

I have edited the answer choices accordingly. Cheers, Brent

rohit8865 · Answer

Ahhh... and i was trying to convert 42 to somehow into 32 but it was quiet difficult to find your fault with numbers provided in stem!!!!!!

AR15J · Answer

Hi  rohit ,

Can you please explain how are you getting this formula?

total volume with cylender inserted - volume of only cylender = volume of water with new height

fireagablast · Answer

Volume big cylinder = 16*6 = 96
Volume internal cylinder = 9*6 = 54
96-54 = 42 --> new volume if cylinder removed

96-54/96 = 42/96 = 7/16 --> new ratio for water 
6/pi * 7/16 = 42/16pi = 21/8pi

LIBERTYRodP · Answer

First, Get the actual volume of water in that area of the big cylinder that is not occupied by the thinner cylinder

1. Water in the big cylinder up to height of 6/pi - Area occupied by thinner cylinder up to 9/pi --->

16 * pi^2 * 6/pi - 9*pi^2 * 6/pi =  42pi

2. Now look for the new Height if the thinner cylinder is removed

Water of cylinder up to a X height = 42pi

16 * pi^2 * X = 42pi

X = 21/8pi

bumpbot · Answer

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A solid cylinder with radius 3 inches sits in a cylindrical

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