' File XIX_dbl12

' Given a sphere: x^2 + y^2 + z^2  --> r^2 + z = 9
' A hole of r = 2 is drilled thrugh the center of the sphere. Assume this hole is
'   a cylinder. Find the volume of the remainding sphere.
' Looking straight down the z-axis. we see that r varies from 2 (cylinder) to 3 (sphere).
pi = 3.14159

F{x,r} = (sqrt[9 - r^2] + sqrt[9 - r^2]) r        ' Cover both halves of cut out sphere.
' ******************************************
a = 0  :  b = 2pi  :  C{x} = 2  :  D{x} = 3
n = 10  : m = n

vx = dblInt[F, C, D, {a, b, n, m,y}]
ex = 20Sqrt[5] pi / 3
er = (ex - vx)100 / ex     ' in percent.


