It is currently 25 Jun 2017, 17:54

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A container in the shape of a right circular cylinder is 1/2

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39673
A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

16 Jul 2012, 04:40
Expert's post
12
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

75% (02:36) correct 25% (01:30) wrong based on 869 sessions

### HideShow timer Statistics

A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

(A) $$\frac{16}{9\pi}$$

(B) $$\frac{4}{\pi}$$

(C) $$\frac{12}{\pi}$$

(D) $$\sqrt{\frac{2}{\pi}}$$

(E) $$4\sqrt{\frac{2}{\pi}}$$

Diagnostic Test
Question: 22
Page: 23
Difficulty: 600
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

16 Jul 2012, 13:07
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
SOLUTION

A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

(A) $$\frac{16}{9\pi}$$

(B) $$\frac{4}{\pi}$$

(C) $$\frac{12}{\pi}$$

(D) $$\sqrt{\frac{2}{\pi}}$$

(E) $$4\sqrt{\frac{2}{\pi}}$$

Since 36 cubic inches of water occupy 1/2 of the cylinder, then the volume of the cylinder is 72 cubic inches.

So, we have that $$volume_{cylinder}=\pi*{r^2}*h=72$$ --> $$\pi*{r^2}*9=72$$ --> $$r^2=\frac{8}{\pi}$$ --> $$r=\sqrt{\frac{8}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$. Hence the diameter equals $$2*(2*\sqrt{\frac{2}{\pi}})=4*\sqrt{\frac{2}{\pi}}$$.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

15 May 2013, 08:47
1
KUDOS
Expert's post
kck wrote:
How do you reach the square root of 8 over pie being = to 2 multiplied the square root of 2 over pie?

Welcome to the club!

$$r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$.

Does this make sense?
_________________
Manager
Joined: 06 Jun 2012
Posts: 82
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V38
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

16 Jul 2012, 13:26

The volume of the cylinder is = hr^2(Pie).
If Half of the volume is equal to 36 than the full volume is 72.
since h =9 divide 72/9(pie) u get r^2=8/Pie or r^2=(4*2)/pie.
so r= 2*Sqrt(2/pie)
Since 2r = diameter => diameter = 4*Sqrt(2/pie)
_________________

Try to make my way to San Jose.

??? class of 2016

Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

20 Jul 2012, 03:27
SOLUTION

A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

(A) $$\frac{16}{9\pi}$$

(B) $$\frac{4}{\pi}$$

(C) $$\frac{12}{\pi}$$

(D) $$\sqrt{\frac{2}{\pi}}$$

(E) $$4\sqrt{\frac{2}{\pi}}$$

Since 36 cubic inches of water occupy 1/2 of the cylinder, then the volume of the cylinder is 72 cubic inches.

So, we have that $$volume_{cylinder}=\pi*{r^2}*h=72$$ --> $$\pi*{r^2}*9=72$$ --> $$r^2=\frac{8}{\pi}$$ --> $$r=\sqrt{\frac{8}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$. Hence the diameter equals $$2*(2*\sqrt{\frac{2}{\pi}})=4*\sqrt{\frac{2}{\pi}}$$.

Hope it's clear.
_________________
Intern
Joined: 23 Oct 2012
Posts: 5
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

29 Oct 2012, 03:46
Hi

Could someone simplify it. I don't get it.

What I understand so far is that the container is half full at 36 cubic = full 72 cubic
Height of container is 9 inches = so container with half full is at 4.5 inches height...

72 = 9
36 = 4.5

after this I get stuck with the explanations that have been given....

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

29 Oct 2012, 03:52
DonCarter wrote:
Hi

Could someone simplify it. I don't get it.

What I understand so far is that the container is half full at 36 cubic = full 72 cubic
Height of container is 9 inches = so container with half full is at 4.5 inches height...

72 = 9
36 = 4.5

after this I get stuck with the explanations that have been given....

Thanks

You don't need to for half-full container after you get that the volume of the whole container is 72 cubic inches.

We have that the volume is 72 cubic inches and the height is 9 inches --> $$volume_{cylinder}=\pi*{r^2}*h=72$$ --> $$\pi*{r^2}*9=72$$ --> $$r^2=\frac{8}{\pi}$$ --> $$r=\sqrt{\frac{8}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$. Hence the diameter equals $$2*(2*\sqrt{\frac{2}{\pi}})=4*\sqrt{\frac{2}{\pi}}$$.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

29 Oct 2012, 05:49
Responding to a pm:

As I wrote in my post "you don't need to go back to half-full container after you get that the volume of the whole container is 72 cubic inches".

The volume of a cylinder is given by: $$volume_{cylinder}=\pi*{r^2}*h$$. We know that it equals to 72 and its height is 9. Substitute these values to get $$\pi*{r^2}*9=72$$ --> divide by 9: $$\pi*{r^2}=8$$ --> divide by $$\pi$$: $$r^2=\frac{8}{\pi}$$ --> take the square root: $$r=\sqrt{\frac{8}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$. Diameter is twice the radius, thus $$d=2*(2*\sqrt{\frac{2}{\pi}})=4*\sqrt{\frac{2}{\pi}}$$.

Hope it helps.
_________________
Intern
Joined: 30 Apr 2013
Posts: 2
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

15 May 2013, 08:45
How do you reach the square root of 8 over pie being = to 2 multiplied the square root of 2 over pie?
Intern
Joined: 30 Apr 2013
Posts: 2
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

15 May 2013, 08:56
Bunuel wrote:
kck wrote:
How do you reach the square root of 8 over pie being = to 2 multiplied the square root of 2 over pie?

Welcome to the club!

$$r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$.

Does this make sense?

Thank you for the welcome and yes it does! Now it seems so simple. Thanks again buddy!
Manager
Joined: 12 Jan 2013
Posts: 219
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

17 Dec 2013, 09:55
Bunuel wrote:
A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

(A) $$\frac{16}{9\pi}$$

(B) $$\frac{4}{\pi}$$

(C) $$\frac{12}{\pi}$$

(D) $$\sqrt{\frac{2}{\pi}}$$

(E) $$4\sqrt{\frac{2}{\pi}}$$

Diagnostic Test
Question: 22
Page: 23
Difficulty: 600

They give us cubic inches ----> 36in^3 and then want us to find find a value that is in inches ---> in^1 .. Why are they not consistent? If they talk about cubic inches then they should also take the cubic root out on both sides... I don't get it.
Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

17 Dec 2013, 09:58
aeglorre wrote:
Bunuel wrote:
A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

(A) $$\frac{16}{9\pi}$$

(B) $$\frac{4}{\pi}$$

(C) $$\frac{12}{\pi}$$

(D) $$\sqrt{\frac{2}{\pi}}$$

(E) $$4\sqrt{\frac{2}{\pi}}$$

Diagnostic Test
Question: 22
Page: 23
Difficulty: 600

They give us cubic inches ----> 36in^3 and then want us to find find a value that is in inches ---> in^1 .. Why are they not consistent? If they talk about cubic inches then they should also take the cubic root out on both sides... I don't get it.

Volume is in cubic inches and the length is in inches. How can length be in cubic inches?
_________________
Manager
Joined: 12 Jan 2013
Posts: 219
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

17 Dec 2013, 13:25
Bunuel wrote:
aeglorre wrote:
Bunuel wrote:
A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

(A) $$\frac{16}{9\pi}$$

(B) $$\frac{4}{\pi}$$

(C) $$\frac{12}{\pi}$$

(D) $$\sqrt{\frac{2}{\pi}}$$

(E) $$4\sqrt{\frac{2}{\pi}}$$

Diagnostic Test
Question: 22
Page: 23
Difficulty: 600

They give us cubic inches ----> 36in^3 and then want us to find find a value that is in inches ---> in^1 .. Why are they not consistent? If they talk about cubic inches then they should also take the cubic root out on both sides... I don't get it.

Volume is in cubic inches and the length is in inches. How can length be in cubic inches?

Wow, that is embarassing. Thanks for the heads up, Ill just blame it on mind fatigue!
Senior Manager
Joined: 13 May 2013
Posts: 469
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

17 Dec 2013, 14:01
A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

I've gotten this question wrong before and I'm still not 100% sure why it's solved the way it is.

If the container is 1/2 full of water and the volume of water is 36 when the total volume is twice that, or 72 inches.

V = pi * r^2 * h
72 = pi * r^2 * (9)
8 = pi * r^2
8/pi = r^2
√8 / √pi = r
d = 2r
d = 2(√8 / √pi)
d = 2√8 / √pi
d = (2 * √8 * √pi) / pi

Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

18 Dec 2013, 01:59
WholeLottaLove wrote:
A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

I've gotten this question wrong before and I'm still not 100% sure why it's solved the way it is.

If the container is 1/2 full of water and the volume of water is 36 when the total volume is twice that, or 72 inches.

V = pi * r^2 * h
72 = pi * r^2 * (9)
8 = pi * r^2
8/pi = r^2
√8 / √pi = r
d = 2r
d = 2(√8 / √pi)
d = 2√8 / √pi
d = (2 * √8 * √pi) / pi

The red part can simplified: $$r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$.
_________________
Senior Manager
Joined: 13 May 2013
Posts: 469
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

18 Dec 2013, 15:49
Ahh...simple mistake! Thanks!

quote="Bunuel"]
WholeLottaLove wrote:
A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

I've gotten this question wrong before and I'm still not 100% sure why it's solved the way it is.

If the container is 1/2 full of water and the volume of water is 36 when the total volume is twice that, or 72 inches.

V = pi * r^2 * h
72 = pi * r^2 * (9)
8 = pi * r^2
8/pi = r^2
√8 / √pi = r
d = 2r
d = 2(√8 / √pi)
d = 2√8 / √pi
d = (2 * √8 * √pi) / pi

The red part can simplified: $$r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$.[/quote]
Manager
Joined: 15 Aug 2013
Posts: 59
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

19 Dec 2013, 04:14
I understand how it is done above. But can someone help me explain what is wrong with below -
Given is a right circular cylinder, which is half full.
V/2 = 36. Also height will be half i.e. 4.5 inches when the culinder is half full.
Hence, (pi*r^2*4.5)/2 = 36. This gives radius = 4/sqrt(pi). This is wrong though.

I am not quite sure what is wrong with this. Can someone explain ?
Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

19 Dec 2013, 04:23
zerosleep wrote:
I understand how it is done above. But can someone help me explain what is wrong with below -
Given is a right circular cylinder, which is half full.
V/2 = 36. Also height will be half i.e. 4.5 inches when the culinder is half full.
Hence, (pi*r^2*4.5)/2 = 36. This gives radius = 4/sqrt(pi). This is wrong though.

I am not quite sure what is wrong with this. Can someone explain ?

It should be $$\pi{r^2}*4.5=36$$, no need to divide by 2, since you already accounted for half of the volume by dividing the height by 2.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15980
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

04 Dec 2015, 13:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15980
Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]

### Show Tags

10 Jan 2017, 17:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A container in the shape of a right circular cylinder is 1/2   [#permalink] 10 Jan 2017, 17:18
Similar topics Replies Last post
Similar
Topics:
3 Volume of a right circular cylinder is 60 l. If radius of cylinder is 1 14 Jun 2016, 09:25
5 A glass is shaped like a right circular cylinder with a half sphere at 4 13 Mar 2017, 10:14
13 A full stationary oil tank that is a right circular cylinder 9 09 Jul 2016, 09:20
3 A soda can, in the shape of a right circular cylinder, is 1 28 May 2012, 02:56
5 A glass is shaped like a right circular cylinder with a half sphere at 12 25 Sep 2015, 08:18
Display posts from previous: Sort by

# A container in the shape of a right circular cylinder is 1/2

 Powered by phpBB © phpBB Group and phpBB SEO 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®.