For the first approximation, the radius of the nose cone is given by the equation (recall, D is assumed to be 1)
r(x) = B - Cx ft
Since the radius is known to be 20 ft at x = 0, the constant B can be determined as
r(0) = B - C(0) => B = 20
At the other end, the nose cone tapers to zero, so at x = 100 ft, the radius is zero. Using this condition, the constant C can be determined,
r(100) = 20 - 100 C = 0
C = 0.2
Based on symmetry, the centroid must lie somewhere along the x axis.