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]

16 Jul 2012, 04:40

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based on 21 sessions

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

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

15 May 2013, 08:47

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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]

16 Jul 2012, 13:07

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]

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]

20 Jul 2012, 03:27

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

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]

29 Oct 2012, 03:52

DonCarter wrote:

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]

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]

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]

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!

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink] 15 May 2013, 08:56

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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

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