(Hopefully)Very quick volume calculation question

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    Calculation Volume
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SUMMARY

The discussion centers on calculating the volume of a truncated cone (cylinder with differing end radii) using the formula V = (πh/3)(R² + r² + Rr). Here, R and r represent the top and bottom radii, respectively, while h denotes the height of the cylinder. The user initially struggled to find a suitable formula but received guidance from another participant, who directed them to the Wikipedia page on frustums. The formula provided effectively addresses the user's query regarding volume calculation.

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  • Understanding of geometric shapes, specifically truncated cones.
  • Familiarity with the formula for volume calculation.
  • Basic knowledge of calculus for derivation purposes.
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  • Research the properties and applications of frustums in geometry.
  • Learn how to derive the volume formula for a truncated cone using calculus.
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Students, educators, and professionals in mathematics, engineering, and design who require knowledge on volume calculations for truncated cones and related geometric shapes.

venomxx
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Iv been looking for a way to calculate the volume of a cyllender with one end radius "x" and the other end with a radius "y".

I know you can do it by considering both circles the base's of 2 cones that when taken away from one another should equal the volume of the cyllender I want. BUT i don't have the height of the cone.

All I have to work with is the radius of the top and bottom of the cyllender and the height of the cyllender...any suggestions? Iv been looking around for a formula or alternate method but i have only found symmetrical cyllender methods.

Sorry for my ignorance if this is a simple answer!
 
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Hi venomxx! :smile:

Check out http://en.wikipedia.org/wiki/Frustum
This gives the formula

V=\frac{\pi h}{3}(R^2+r^2+Rr)

where h is the height of your truncated cone, and where R and r are the two radii.

Do you need to prove this formula too? In that case, it's easiest when you know some calculus...
 
Cheers for the quick reply micromass! That formula is giving me exactly what I needed! Ill give it a shot deriving it myself:)
 

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