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Two cylinders... area?

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Two cylinders... area?

by zyarkz » Sun Nov 23, 2008 2:49 pm
Two cylinders are made from metal. One cylinder has a height of 5h inches and a radius of r inches. The other has a height of h inches and a radius of 2r inches. The two cylinders are melted and the molten metal recast as a single cylinder of height h inches without wasting any of the metal. What is the radius of the new cylinder?

r inches
3r inches
4r inches
8r inches
9r inches
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by mals24 » Sun Nov 23, 2008 3:02 pm
IMO 3r inches

Since the cylinder is made from the same metal which the other 2 cylinders are made, the volume of the new cylinder will be equal to the combined volume of the 2 cylinders. This is so because of the amount of metal used to make the new cylinder is equal to the amount of metal used to make each of the 2 cylinders.

Let the radius of the new cylinder = A
Volume of cylinder = Pi(h*r^2)

Pi(5h*r^2)+Pi(h*4r^2) = Pi(h*A^2)
5r^2 + 4r^2 = A^2

9r^2 = A^2
A = 3r
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by 4meonly » Mon Nov 24, 2008 1:12 am
What is the source of the question?

To melt means to dissolve, that's why new cylinder has the area of the surfce equal to the sum of the surfaces on two cylinders.
Also we are limeted not by the volume but by the amount of metal.

I agree that if we will calculate through volume we will get 3.
But here it is not correct to calculate through volume.
IMHO

Any opinion?
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by orel » Mon Nov 24, 2008 1:28 am
4meonly wrote:What is the source of the question?

To melt means to dissolve, that's why new cylinder has the area of the surfce equal to the sum of the surfaces on two cylinders.
Also we are limeted not by the volume but by the amount of metal.

I agree that if we will calculate through volume we will get 3.
But here it is not correct to calculate through volume.
IMHO

Any opinion?
why do you think it is incorrect to calculate it by volume?
the problem says without wasting any of the metal, so, using volume should be the way of calculating it.
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by mals24 » Mon Nov 24, 2008 3:43 am
@4meonly
Your right the surface area will also be the same. The volume and the surface area both will be the same.

Volume is the space an object occupies.

Take for instance 2 ice cubes. You melt the 2 ice cubes and combine the water and freeze that water to make a single ice cube. Now the space this 1 ice cube will occupy will be equal to the combined space the other 2 ice cubes would occupy right.

Same for the new cylinder. The space that the new cylinder will occupy will be equal to the combined space of other 2 cylinders.
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