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A cylinder is being filled with sand weighing 200 kg per cub

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A cylinder is being filled with sand weighing 200 kg per cub [#permalink] New post 17 Feb 2013, 09:01
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A cylinder is being filled with sand weighing 200 kg per cubic foot. The cylinder has a diameter of 1 foot and is 5 feet tall. How much sand is being used??

A 250pi kg
B 500pi kg
C 500pi^2 kg
D 1000pi kg
E 1000pi^2 kg
[Reveal] Spoiler: OA
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Re: A cylinder is being filled [#permalink] New post 17 Feb 2013, 09:33
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Hi,

Lots of geometry questions! The area of a cylinder is Pi*Radius^2*Height. A cylinder is like a bunch of circles stacked on top of each other and that is where the height comes in. So in this case (to find the volume) you need to find the area of the circle: (.5^2)*Pi and multiply that by the height of 5. So the volume is 5/4PI cubic feet. That's how much sand you need to fill the cylinder. Now, you know that the sand weighs 200Kg per cubic foot. So, multiply 200 by 5/4Pi and you get 250Pi Kg.

Let me know if this makes sense to you.

HG.
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Re: A cylinder is being filled [#permalink] New post 17 Feb 2013, 09:53
Expert's post
Answer is A.

Volume of Cylinder = Pi*r^2 *h --------> Pi * (1/2)^2 * 5 --------> Pi * (1/4) * 5 --------> (5/4)Pi cubic feet.
1 cubic feet = 200 kg. so (5/4)Pi cubic feet = ((200*5)/4)Pi ---------> 250Pi

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Last edited by Narenn on 17 Feb 2013, 12:25, edited 1 time in total.
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Re: A cylinder is being filled [#permalink] New post 17 Feb 2013, 11:33
Thanks guys.

I realized my screwup. My brain tends to turn to fog toward the end of study sessions.
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Re: A cylinder is being filled with sand weighing 200 kg per cub [#permalink] New post 20 Feb 2013, 13:20
Volume of a cylinder is pi(r)^2 x h.
r = 1/2, h =5
Therefore volume = 5pi/4....take this volume and multiply by 200. You get 250pi. (A)
Re: A cylinder is being filled with sand weighing 200 kg per cub   [#permalink] 20 Feb 2013, 13:20
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A cylinder is being filled with sand weighing 200 kg per cub

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