Surface area

Question

Surface area

anonymous · Answer

attachment

anonymous · Answer

Ok so I have worked out this problem several times and my answer is 2 pie. However I feel like its incorrect! Not sure what I'm doing with this one

anonymous · Answer

$$2\pi \int\limits_{-5}^{5}\sqrt{100-y ^{2}}\sqrt{\frac{ y ^{2} }{ (10-y)(10+y) }}$$

anonymous · Answer

This was my last step before I plugged in my numbers

hartnn · Answer

is that just f'(x)^2 ?
if i can recollect, isn't there 1+f'(x)^2 in the formula ?

anonymous · Answer

yes thats correct. What i had written up there was the derivative squared already

anonymous · Answer

oh whoops i see i did forget the 1 but i do have the one written on my paper!

hartnn · Answer

ok, cool.

anonymous · Answer

ok! SO.. i think i may have found my mistake here is my new answer ...

anonymous · Answer

$$20\pi \sqrt{\frac{ 5 }{ 3 }}-20\pi$$

hartnn · Answer

why i am i getting 200pi then

anonymous · Answer

eeeek I have no idea :/

hartnn · Answer

that 1+ y^2/(100-y^2) 
comes out to be 

100/(100-y^2)

and that 100 -y^2 in the denominator cancels out with sqrt(100-y^2) outside, leaving just 10......ehh, let me draw it out

hartnn · Answer

|dw:1391325764071:dw|
sorry for that artistic drawing :P