Why Do Sphere Surface Areas Differ With Same Approximation?

[joseph_seb]

i have found the area of sphere in two ways using the same approximation.but i get two different answers ;one the correct value 4∏R^2?how does this happen?
i'm attaching the solution below?please refer to the attachments and give a solution?

 

[HallsofIvy]

Your mistake is where "transform the frustrum to a cylinder". You don't actually do a "tranformation" you just assume frustrum is equal to the cylinder and that is not true.

 

[joseph_seb]

i only assumed r1=r2(same approximation in both methods);then the frustum automatically transformed to cylinder.chekout the following links-
1.http://i.imgur.com/NJJa8.jpg
2.http://i.imgur.com/MVmff.jpg
or
http://www.filedropper.com/sphere

 

[slider142]

You write dA = 2Pirh and h = rsin(theta)dtheta, but then you write dA = 2Pir^2 sin^2(theta) dtheta. Where does the extra sin(theta) come from?