Simple Question: Volume -> Diameter

In summary, To find the diameter of a sphere using the volume, use the formula d = \sqrt[3]{\frac{6V}{\pi}} where V is the volume of the sphere. This is derived from the formula for the volume of a sphere, V = \frac{4}{3}\pi \Big(\frac{d}{2}\Big)^3.
  • #1
bbg5000
14
0
Simple Question: Volume --> Diameter

I know how to find volume using diameter, but how do you find diameter using volume?
 
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  • #2
The volume of what? A sphere? A cylinder? A cone?

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

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

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

cookiemonster
 
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  • #5
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.
 
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  • #6
Hah, hah, hah... Did I do that?

cookiemonster
 
  • #7
Thanks for the help cookiemonster...
 
  • #8
Gah... Minor details.

cookiemonster
 

What is the relationship between volume and diameter?

The relationship between volume and diameter is an inverse relationship, meaning that as one increases, the other decreases. This relationship can be represented mathematically as V = k/d^3, where V is volume, k is a constant, and d is diameter.

How does the diameter affect the volume of an object?

The diameter of an object has a significant impact on its volume. As the diameter increases, the volume also increases, and vice versa. This is because the volume of an object is directly proportional to the cube of its diameter.

What is the formula for calculating volume from diameter?

The formula for calculating volume from diameter is V = π/6 * d^3, where V is volume, π is the mathematical constant pi, and d is diameter. This formula applies to objects with a circular cross-section, such as cylinders and spheres.

What is the unit of measurement for volume and diameter?

The unit of measurement for volume is typically cubic units, such as cubic meters or cubic inches. The unit of measurement for diameter is typically length units, such as meters or inches. However, it is essential to use consistent units for both volume and diameter when calculating or comparing values.

Can volume and diameter be used to determine the shape of an object?

No, volume and diameter alone cannot determine the shape of an object. There are many different shapes that can have the same volume and diameter, such as a sphere and a cube. To determine the shape of an object, other measurements and characteristics, such as height and surface area, must also be considered.

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