sir, the area of this curved surface(part of sphere) is obtained by assuming the width of ring as Rd(phi) which I understand.
but is the area of flat circular surface which is called base of cone is (pi/2)(R^2)(1-cos(2(phi)))
which is obtained by taking width of ring as dx where x=Rsin(phi)
and so dx=Rcos(phi)d(phi)
then area of flat circular surface
S=integration 0 to (phi) of 2(pi)xdx
which is
S=integration 0 to (phi) of 2(pi)(Rsin(phi))(Rcos(phi)d(phi))
and if all this is correct then equating it with S=(omega)(R^2) we get
(omega)=((pi)/2)(1-cos(2(phi)))
which contradicts the original result. kindly elaborate.
6 years ago
by
bruce wayne