How Do You Calculate Diameter from Volume?

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Discussion Overview

The discussion revolves around the question of how to calculate the diameter of a sphere from its volume. Participants explore the relevant formulas and clarify the relationships between volume and diameter.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks how to find the diameter of a sphere given its volume.
  • Another participant points out the need to clarify the shape in question, initially asking if it is a sphere, cylinder, or cone.
  • A participant provides the formula for the volume of a sphere in terms of diameter and suggests solving for diameter.
  • Another participant corrects the previous claim, indicating that the radius should be cubed, not squared, and that the final formula would need to reflect this correction.
  • There is a light-hearted acknowledgment of the mistake by the original poster.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the final formula for diameter, as there is a correction regarding the use of radius and the mathematical operations involved.

Contextual Notes

The discussion includes potential errors in mathematical expressions and assumptions about the shape being discussed, which may affect the accuracy of the derived formula.

bbg5000
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Simple Question: Volume --> Diameter

I know how to find volume using diameter, but how do you find diameter using volume?
 
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The volume of what? A sphere? A cylinder? A cone?

cookiemonster
 
..whoops...yeah, a sphere. How do you find the diameter of a sphere using the volume?
 
V = \frac{4}{3}\pi \Big(\frac{d}{2}\Big)^3

That's the formula for the volume of a sphere in terms of the diameter. Now just solve for d!

d = \sqrt[3]{\frac{6V}{\pi}}

cookiemonster
 
Last edited:
Cookiemonster probably meant to cube his radius, not to square it, and thus also to use a cube root, not a square root. This would change his final formula slightly.
 
Last edited:
Hah, hah, hah... Did I do that?

cookiemonster
 
Thanks for the help cookiemonster...
 
Gah... Minor details.

cookiemonster
 

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