Thread: Areas of surfaces.

Here's my question:

Find the area of the surface created by the complete curve r=a when it is completely revolved about the x axis.Do not assume the formula for the surface area of a sphere.

Just by looking at it I did:



Which was incorrect.

So then I did it the way I think I was supposed to:



and this answer was also wrong. The book gave the answer as:



What's going wrong??

Originally Posted by Showcase_22

Here's my question:

Find the area of the surface created by the complete curve r=a when it is completely revolved about the x axis.Do not assume the formula for the surface area of a sphere.

Just by looking at it I did:

Mr F says: *Ahem* You're rotating a circle around the x-axis. This gives a sphere. You do recall that the surface area of a sphere is , don't you?

Which was incorrect. Mr F says: Obviously.

So then I did it the way I think I was supposed to:



and this answer was also wrong. The book gave the answer as:



What's going wrong??

The formula is .

So for your problem .

That's why your answer is wrong by a factor of 2.

I wasn't visualising it correctly. I was thinking of it in 2D form and not 3D.

When it's a 2D circle and it's rotated around the x axis, it only needs to be rotated by pi radians and not 2pi.

Thanks Mr Fantastic!