The figures above show a sealed container that is a right circular cyl

Question

https://gmatclub.com/forum/download/file.php?id=47605 The figures above show a sealed container that is a right circular cylinder filled with liquid to \frac{1}{2} its capacity. If the container is placed on its base, the depth of the liquid in the container is 10 centimeters and if the container is placed on its side, the depth of the liquid is 20 centimeters. How many cubic centimeters of liquid are in the container? A. 4,000\pi B. 2,000\pi C. 1,000\pi D. 400\pi E. 200\pi PS16602.01 Quantitative Review 2020 NEW QUESTION 2019-04-26_1800.png

ShukhratJon · Accepted Answer

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ak31 · Answer

cylinder is filled half its capacity. therefore, volume of cylinder =  \pi  r^{2} h and volume of liquid is  \pi  r^{2} h/2
When cylinder is at base the volume of liquid = 10 \pi  r^{2} . This is half the capacity. therefore, full capacity = \pi  r^{2} 20
this gives us the height of the cylinder (h)= 20
when cylinder is at side then r=h. therefore, volume of container =  \pi  20^{2} 20 = 8000 \pi .

we are asked to find out the volume of liquid which is half the capacity of cylinder = 1/2 x8000 \pi  = 4000 \pi

Archit3110 · Answer

see 2nd fig here h=r=20 so
vol pi * r^3; 8000 pi
given that vol of liquid half capacity of container ; 8000*pi/2 = 4000 pi
IMO A

Anisha1308 · Answer

Hey can you explain why r=h when cylinder is placed at side?

CEO2021 · Answer

Anisha1308

Since it is filled half of its capacity,it will be half filled all the way one rotates the cylender.
But we r given that cylendar is now 90 DEG placed of original position so ...now the height is what the radius was in first case.
Thus ,r=h when cylinder is placed at side

MHIKER · Answer

When the container is placed on its base, the depth of the liquid in the container is  10  centimeters = height of the liquid

When the depth of the liquid is  20  centimeters = radius of the liquid

The volume =  \pi  r^2*h 
 =  \pi  20^2*10 
   =   \pi  4000

The Answer is A.

adityaganjoo · Answer

The diagrams tell us everything we need.
Second diagram gives the radius = 20;
First one gives us the height = 10;
Considering that both of them are the same cylinders, we can compute the volume as  (20*20*10\pi)  =  4,000\pi 
Therefore, (A)

all  Please do let me know if I am missing anything here

woohoo921 · Answer

Bunuel 
Why can we say that that the radius is 20 of just the liquid when we can see than 20 is the radius of the whole container? So, in order words, why don't we need to take 1/2 of 20? Not taking 1/2 of the height makes sense to me because we can see the liquid is not up all the way. Thanks!

Bunuel · Answer

We are told that the container is filled to  half  its capacity. When the container is on its side, so when the diameter of the circular side becomes the height of the container, the depth of the liquid will reach the half of the diameter, so the depth = d/2 = r.

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The figures above show a sealed container that is a right circular cyl

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The figures above show a sealed container that is a right circular cyl

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