B Need some clarification to get dimensions for a volume

[AjaxOfTheRockies]

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]

 

[PeroK]

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 $0.027 \ cm^3$.

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.

 

[AjaxOfTheRockies]

Thanks for the info. On the cylinder, I was thinking of one near equal width/length

 

[PeroK]

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 $\pi \dfrac{l^3}{4}$.

 

[AjaxOfTheRockies]

Excellent! Thank you!!

 

[Lnewqban]

... 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.