Problem 51 Solution

The radius of the base of the cone is (360-x)/360.

The height of the cone is (1-((360-x)/360)²)^1/2.

The area of the cone is 1/3*pi*radius²*height.

Let u=((360-x)/360)².

The area becomes: pi/3 * (1-u)^1/2 * u.

Take the deriviate and set equal to 0: u=2/3.

If u=2/3 then x=360*(1-(2/3)^1/2).

Thus the radius = (2/3)^1/2.

Thus the height = 3^-1/2.

The area of the cone is (2*pi)/(9*3^1/2) =~ .403.

Thanks for "Roeterink" for correcting me first answer.

Michael Shackleford, A.S.A.