B Need some clarification to get dimensions for a volume

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The discussion revolves around converting a volume of 0.04 cubic centimeters into usable dimensions for a shop project. A cube with this volume was initially calculated to have sides of approximately 3mm, but this was corrected to 3mm yielding a volume of only 0.027 cc. The main query then shifted to determining the dimensions of a cylinder with the same volume, where the shape can vary significantly depending on the desired proportions. It was suggested that for a cylinder with equal length and diameter, the volume can be calculated using the formula for the volume of a cylinder, which relates the length and diameter. Practical advice included measuring the internal diameter of an available cylinder to calculate the necessary height for the desired volume.
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I have a volume of 0.04 cubic centimeters. I need to convert into something I can work with in my shop. Tolerance is not important.

To get dimensions of a cube with this volume, I calculated the cube-root which came out to 0.341. So, my cube would be (rounded) 3mm on a side, correct?

Next question, is what dimensions would a cylinder of 0.04 cc be? That one left me completely stumped. I see lots of instruction online on how to take a dimensions of a cylinder and calculate the volume, but nothing on the reverse.

Thanks!!

—A

[edited to correct my starting number]
 
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AjaxOfTheRockies said:
I have a volume of 0.04 cubic centimeters. I need to convert into something I can work with in my shop. Tolerance is not important.

To get dimensions of a cube with this volume, I calculated the cube-root which came out to 0.341. So, my cube would be (rounded) 3mm on a side, correct?
A cube of side length ##3 \ mm## would have a volume of ##0.3^3 \ cm^3##, which is ##0.027 \ cm^3##.
AjaxOfTheRockies said:
Next question, is what dimensions would a cylinder of 0.04 cc be? That one left me completely stumped. I see lots of instruction online on how to take a dimensions of a cylinder and calculate the volume, but nothing on the reverse.
It depends on the shape of your cylinder: long and thin or short and fat. There are lots of different cylinders with that volume, all with a different shape.
 
Thanks for the info. On the cylinder, I was thinking of one near equal width/length
 
AjaxOfTheRockies said:
Thanks for the info. On the cylinder, I was thinking of one near equal width/length
If the length and diameter of the cylinder are both ##l##, then the radius is ##\dfrac l 2##. The cross-sectional area is ##\pi (\dfrac l 2)^2## and the volume is ##\pi \dfrac{l^3}{4}##.
 
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Excellent! Thank you!!
 
AjaxOfTheRockies said:
... On the cylinder, I was thinking of one near equal width/length
Just a relation that you may find interesting:

https://www.mathsisfun.com/geometry/cone-sphere-cylinder.html

In practical terms, I would carefully measure the internal diameter of a suitable cylinder that you may have available, and then calculate what height achieves the desired volume you need to work with in your shop.
 
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