How do you calculate volume of cylinder in taper shape?

Answer 1

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.

KK

or you can just average the two radius' and use the averaged radius in the familiar pi*a^2*h...a bit easier