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Posted by Bill
on 3/7/2009, 12:11 pm, in reply to "Care to share?"
Integrate w.r. to the inclined surface ds rather than the horixontal projection dx.
At x = h y = k so a = k^2/4h
ds = sqrt(dx^2+dy^2) = dx.sqrt(1+(dy/dx)^2)
dA = 4Pi.sqrt(a).sqrt(a+x).dx
A = 4Pi.sqrt(a).2/3(a+h)^(3/2)-a^(3/2))
Substitute a = k^2/4h
A = Pi.k/(6.h^2).(k^2+4.h^2)^(3/2)-k^3).
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