# Need some clarification to get dimensions for a volume

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• AjaxOfTheRockies
In summary, there is a volume of 0.04 cubic centimeters that needs to be converted into a workable form for a shop. The cube-root of 0.04 is approximately 0.341, so a cube with side length 3mm would have a volume of 0.027 cubic centimeters. As for a cylinder with the same volume, the dimensions would depend on the shape of the cylinder. If the length and diameter are equal, the radius would be half the length and the volume would be π times the cube of the radius divided by 4. Alternatively, one could carefully measure the internal diameter of a suitable cylinder and calculate the needed height to achieve the desired 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]

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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.

Lnewqban
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.

## 1. What is the definition of volume?

Volume is the amount of space occupied by an object or substance. It is typically measured in cubic units, such as cubic meters or cubic feet.

## 2. How do I calculate the volume of a regular object?

To calculate the volume of a regular object, you can use the formula V = l x w x h, where V is the volume, l is the length, w is the width, and h is the height. Make sure all measurements are in the same unit before multiplying.

## 3. How do I find the volume of an irregular object?

To find the volume of an irregular object, you can use the water displacement method. Fill a graduated cylinder with water and record the initial volume. Then, submerge the object in the water and record the new volume. The difference between the two volumes is the volume of the object.

## 4. What are some common units of measurement for volume?

Some common units of measurement for volume include cubic meters, cubic centimeters, liters, gallons, and cubic feet. The unit used will depend on the size and type of object being measured.

## 5. How do I convert between different units of volume?

To convert between different units of volume, you can use conversion factors. For example, 1 liter is equal to 1000 cubic centimeters. So to convert from liters to cubic centimeters, you would multiply the number of liters by 1000. You can find conversion factors online or in a conversion chart.

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