How to calculate volume of a weird cylinder (decreasing radius) NEED HELP FAST?

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maranello993

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Ok, so I need to get the formula for the volume of a cylinder that starts with a radius, say 1.5, and ends with a radius, say .75. The length will be 2. Is there a formula for this? Is there a name for this shape?
You guys are awesome. Quick response, you have no idea how relieved I am right now! You have saved me much time and stress! Thank you so much!
 
Any tapered cylinder can be treated as a [longer cone] minus a [smaller cone]. Lets say the cylinder we need the volume for has the following dimensions:
height=h2
base radius=a
top radius=b

volume of this cylinder = volume of cone with base radius of 'a' and height 'h1+h2' minus the volume of a smaller cone with base radius 'b' and height 'h1'

where, the heights and the radii are obviously related by h1/b = (h1+h2)/a

so the volume we need = pi*a^2*(h1+h2)/3 - pi*b^2*h1/3
and this simplifies to pi*h2*(a^2+a*b+b^2)/3

easy to verify: if a=b then it should be the familiar pi*a^2*h which is what the above formula gives.
 
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