A trough of length & has a cross section in the shape of a semicircle with radius r (See Fig).
When filled with water to within a distance h of the top, the volume V of water is V = L[0.5pi * r ^ 2 - r ^ 2 * arcsin(h/r) - h * (r ^ 2 - h ^ 2) ^ (1/2)]
Suppose L = 10ft, r = 1ft and V = 12.4f * t ^ 3 Find the depth of water in the trough to within 0.01 ft. (Use Newton's Method)
