Thread: [SOLVED] Creating a frustum cone from a frustum cone

hi, Im trying to calculate the volume of a frustum of a frustum of a cone. I understand how to calculate the volume of a frustum cone, but i need to make a frustum of the frustum cone( if that makes sense) Basically, if you imagine a frustum of a cone shaped vessel, that is partially full of liquid, im trying to calculate the volume of liquid, given;

top radius ( Rt )
bottom radius ( Rb )
height of vessel ( H )
height of fluid in vessel (measured from bottom). ( h )

I haven't done any trig for many years, and the best i could come up with was calculating the new top radius given the height of the fluid, then calculating the new volume should be easy. So far i have:

new top radius = Rb + (2 ( (H - h) * (Tan(arcTan((H / ((Rb - Rt) / 2)))))))

and the new top radius is then used to calculate the new frustum cone volume.

is there an easier way? it just seems a bit over complex to me

Originally Posted by manic

... Basically, if you imagine a frustum of a cone shaped vessel, that is partially full of liquid, im trying to calculate the volume of liquid, given;

top radius ( Rt )
bottom radius ( Rb )
height of vessel ( H )
height of fluid in vessel (measured from bottom). ( h )

I haven't done any trig for many years, ...
is there an easier way? it just seems a bit over complex to me

Maybe I've found an easier way to calculate the new radius.

I've attached a sketch of the situation.

Use similar triangles. To be accurate use similar right triangles. You can setup the following proportions:
1)

....... Since all values of the RHS are known you can calculate the length of x.

2)

....... Plug in the value of x from 1) and solve for

I have the same problem to calculate the volume but my cone is rotated 90 degrees. The height of the level of water inside the cone is known but how can i calculate the volume of liquid inside the cone ?