The two bases of a right conical frustum have radii r and R The frustum has \(\frac{2}{3}\) the volume of a cylinder with the same height as the frustum and a radius of R Compute r/R.
+128399 Volume of the cylinder = pi * R^2 * h
So the frustum's volume = (2/3)* pi * R^2 * h (1)
Volume of a frustum = (1/3) * pi * h * [ R + r + Rr ] (2)
Set (1) = (2)
(2/3)pi*R^2*h = (1/3)pi * h * [ R + r + Rr ] simplify
2R^2 = R + r + Rr
2R^2 - R = r + Rr
R (2R - 1 ) = r (1 + R)
R ( 2R - 1 ) / (1 + R) = r
r / R = R(2R - 1) / [ (1 + R) * R ] =
(2R - 1) / (R + 1)
