So most likely I am the one with a mistake...but hell I can't get it to work.

I am attaching my work. So I try to derive the volume of a cylinder from the area of the circle (A(circle) = pi*r^2)....from h=0 to h=H.

Same with the cone...but here we know that the radius depends on the h so A(circle_for_the_cone)= A(h) = (R/H)*h, you derive it and gold.

So I did the same with the cone but changing the integral limits....and doom! Cant get it to work. Could somebody help me out using this methodology???

The volume of the frustrum should be: V (frustrum)= pi*h/3*(R1^2+R1*R2+R2^2)

Check attached picture!

Thanks!