# Why surface area of sphere differ when find in two ways using the same approximation?

1. Mar 23, 2012

### 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?

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• ###### spherearea2.jpg
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2. Mar 23, 2012

### HallsofIvy

Staff Emeritus
Re: Why surface area of sphere differ when find in two ways using the same approximat

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.

3. Mar 24, 2012

### joseph_seb

Last edited: Mar 24, 2012
4. Mar 24, 2012

### slider142

Re: Why surface area of sphere differ when find in two ways using the same approximat

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?

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