Cylinder in Cone

[nycmath]

See attachment

[Guest]

Hi its Bob,

The small cone sitting on top of the cylinder is simmilar to the whole cone. It has radius [tex]r[/tex] and height [tex]H - h[/tex], so

[tex]\frac{H-h}{r} = \frac{H}{R}[/tex]

which gives [tex]h = \frac{H(R-r)}{R}[/tex].

Now substitue into [tex]V = \pi r^2 h[/tex]:

[tex]V(r) = \frac{\pi H r^2 (R-r)}{R}[/tex], where [tex]0 < r < R[/tex].