GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jul 2018, 11:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A closed cylindrical tank contains 36pi cubic feet of water

Author Message
TAGS:

### Hide Tags

Intern
Joined: 10 Apr 2015
Posts: 16
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

### Show Tags

18 Aug 2015, 12:14
Extending the question - what if water is not half of the capacity or an easy number like 1/2 or 1/4 or 1/8. what is the shape of water when cylinder is placed on its side?
Intern
Joined: 10 Aug 2015
Posts: 33
Location: India
GMAT 1: 700 Q48 V38
GPA: 3.5
WE: Consulting (Computer Software)
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

### Show Tags

03 May 2016, 09:39
Bunuel wrote:
A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

Notice that some editions of OG have a typo saying that the height of the water in the tank is 2 feet, it should read "the height of the water in the tank is 4 feet".

We are given 36pi occupies half the volume of the cylinder.
Now it does not matter in what orientation we keep the cylinder. half the volume will always occupy half the cylinder.
Now when cylinder is upright then half of its height is 4 feet bcz water occupies half the cylinder space. Refer to Bunuel's diagrams.
But when we place cylinder horizontal to the ground the diameter of the circle becomes the new height.
Now again the water should occupy half the cylinder space.
So it should occupy the radius length above the ground.
we know 1/2 pi*r^2*h=36 where h =8.
Hope this helps.
Intern
Joined: 19 Nov 2016
Posts: 16
Schools: Erasmus '18
A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

### Show Tags

10 Jan 2017, 04:35
This is my approach.
Regardless of the shift of the cylinder the h (height) and r (radius) , will remain always the same.
V= 36π (volume of water when cylinder is filled in half capacity) --> so the max volume of the cylinder is 2 ∗36π =72π

Volume = π∗r^2∗h (The question asks for the radius in a confusing way) Here we have to notice that the new height = radius of cylinder ,so max volume is :
72π=π∗r^2∗8 (since its h= 4 feet when half capacity-->h=8 will be on full capacity)
72=8∗r^2
r^2=72/8
r^2=9
r= 3

Kudos if u like, keep up the hard work
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2679
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

### Show Tags

11 Jan 2017, 07:51
1
Bunuel wrote:
A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

We are given that a closed cylindrical tank that is half full contains 36π cubic feet of water, and the height of the water is 4 feet. We can thus say that the full tank would have 72π cubic feet of water at a height of 8 feet. Using the volume formula, we can now determine the radius of the circular base:

volume = π(r^2)h

72π = π(r^2)(8)

9 = r^2

r = 3 feet

We see that the radius is 3 feet.

We need to determine the height of the water when the tank is placed on its side on level ground. When the cylinder is turned on its side, the diameter now represents the new height, and since the tank is half full, the new height of the water is equivalent to the radius, so the new height of the water is 3 feet.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 30 Jan 2014
Posts: 2
Location: Qatar
GPA: 2.97
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

### Show Tags

22 Feb 2017, 22:25
My OG - 2013 has a typo of height has "2"
Director
Joined: 09 Mar 2016
Posts: 656
A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

### Show Tags

28 Apr 2018, 09:04
Bunuel wrote:
SOLUTION

Notice that some editions of OG have a typo saying that the height of the water in the tank is 2 feet, it should read "the height of the water in the tank is 4 feet".

A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

Look at the diagram below:

Since the tank is half full when placed upright then naturally it'll also be half full when placed on its side, so the level of the water (when placed that way) will be half of the diameter, so $$r$$.

Now, given that $$V_{water}=\pi{*r^2}*H_{water}$$ --> $$36\pi=\pi{r^2}*4$$ --> $$r=3$$.

Bunuel hello -

"36pi cubic feet of water" doest it mean area is 36pi ?

I found this link and it has something similar but formula is hard to understand very complicated unlike yours https://www.mathopenref.com/cylindervolpartial.html

any difference between your formula method/ and the one described in the link ?

have a great weekend
Manager
Joined: 25 May 2016
Posts: 64
Location: Singapore
Concentration: Finance, General Management
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

### Show Tags

29 Jun 2018, 03:25
Volume of cylinder = pi*r^2*h = pi * r^2 * 4 ft = 36 pi
r^2= 9 pi
r=3ft
A cyl which is half full, placed on its side will also be filled up to half its height which is r.

Therefore, r = 3ft.
_________________

16 Kudos left to unlock next level. Help me by Contributing one for cause .. Please

Manickam

If you found my post helpful, kindly press "+1 Kudos" to appreciate

Re: A closed cylindrical tank contains 36pi cubic feet of water &nbs [#permalink] 29 Jun 2018, 03:25

Go to page   Previous    1   2   [ 27 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.