Solving for radius of a combined shape of a cone and a cylinder where the cone is base is concentric with the cylinder? I have a solid that is a combined shape of a cylinder and a concentric cone
(a round sharpened pencil would be a good example)
Know values are:
Total Volume = 46,000
Height to Base Ratio =  2/1
(Height = cone height + cylinder height) (Base = Diameter)
Angle of cone slope  =  30 degrees (between base and slope of cone)
How do you solve for the Radius?
2  let say the ratio is from the orignal length 
Know value:
Total Volume = V = 46,000
Original Height to Base Ratio = t =  2/1
(Height = cone height + cylinder height + distance shortened) (Base = Diameter)
Angle of cone slope  = θ =  30 degrees (between base and slope of cone)
distance shortened from original Height x = 3 
(Let h be the height of the cylinder. Then h+rtanθ+x=2(2r)
How do you solve for the Radius?

Cone height = $ \sqrt 3 R$. 
Cylinder height = Total height - Cone heght 
$$= (4 -\sqrt3 R ) $$
Total Volume 
$$ V_{total} = V_{cone}+ V_{cyl  } =  \pi R^2 [ (4- \sqrt 3) R ] + \frac\pi3 R^2 \cdot \sqrt3 R = 46000. $$
from  which only unknown $R^3, R $ can be calculated.
