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

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21 00:00

Difficulty:   25% (medium)

Question Stats: 79% (02:04) correct 21% (02:14) wrong based on 1371 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

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Math Expert V
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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6
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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.
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GMAT 1: 710 Q49 V38 Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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)
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 56307
Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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.
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Math Expert V
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Posts: 56307
Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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.
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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How do you reach the square root of 8 over pie being = to 2 multiplied the square root of 2 over pie?
Math Expert V
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Posts: 56307
Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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?
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 56307
Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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?
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Posts: 145
Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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: 414
Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 56307
Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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: $$r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}$$.
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 56307
Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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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.
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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

Recall that the volume of a cylinder is:

Since half of the capacity of the cylinder is 36, the full capacity of the cylinder is 72; thus:

72 = πr^2(9)

8/π = r^2

√(8/π) = r

√8/√π = r

(2√2)/√π = r

2√(2/π) = r

The diameter is twice the radius. Thus, the diameter is 2 x 2√(2/π) = 4√(2/π).

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