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

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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?

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

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

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

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

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


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Difficulty: 600

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

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New post 16 Jul 2012, 13:07
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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 \(2*(2*\sqrt{\frac{2}{\pi}})=4*\sqrt{\frac{2}{\pi}}\).

Answer: E.

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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New post 16 Jul 2012, 13:26
the answer is E.

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

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

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

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

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

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

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

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

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

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New post 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

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

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New post 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

:oops:


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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New post 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

:oops:


The red part can simplified: \(r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}\).[/quote]
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Re: A container in the shape of a right circular cylinder is 1/2  [#permalink]

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

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

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New post 21 Jan 2018, 20:02
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:

volume = π(radius)^2(height)

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).

Answer: E
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Re: A container in the shape of a right circular cylinder is 1/2 &nbs [#permalink] 21 Jan 2018, 20:02
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