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I want to convert a cylinder shape to a cube shape with the same volume but with $1$ height.

If a cylinder with a diameter of $2$ and length of $2$, what are the length and width of a cube when the given height is $1$ and the volume is same with the cylinder?

Can anybody explain how to get the length and width of the cube?

Thank you.

user729424
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Syed Nazri bin Wan Ikhsan
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  • The volume of the cylinder is $\pi rh$, $r=1,h=2$. So, $V_{cylinder}=2\pi$. Note you don't get a cube, since the volumes are the same - so one side of the cube is $\sqrt{2\pi}\ne1$. –  Mar 06 '14 at 02:55
  • Thank you for the respond Sanath, I'm not good with math but I wanted to know what if, a clay shaped in cylinder form with diameter of 2 and the length of 2 then reshaped in rectangular cube form. With a minimum height of 1, what are the length and width of the clay when its transformed from cylinder form into a cuboid form? – Syed Nazri bin Wan Ikhsan Mar 06 '14 at 08:34
  • Then you should ask that question, not the one you did. As the cube root (not the square root) of $2 \pi$ is greater than $1$, the cube proposed by user22283 works well. If you ask about a cuboid, you have one equation in three unknowns so there is not a unique answer. – Ross Millikan Mar 02 '20 at 04:32

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As the cube root (not the square root) of $2 \pi$ is greater than $1$, the cube proposed by user22283 works well. If you ask about a cuboid, you have one equation in three unknowns so there is not a unique answer.

Ross Millikan
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