How Do You Apply the First Theorem of Pappus-Guldinus to Calculate Surface Area?

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Homework Statement


hey, I'm having issues with a problem, and my book doesn't seem to show me how to do it.
so,
i have a curve x = ky^2 and I'm to rotate it about the x-axis. I need to find the surface area generated.

How do i use the first theorem to do this? Thanks for the help

sorry i don't have a pic of the problem. but if you want to see here's a link to my book:
http://books.google.com/books?id=l-...&hl=en&sa=X&oi=book_result&resnum=1&ct=result

problem number 5.60
thanks once again

Homework Equations





The Attempt at a Solution

 
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O011235813 said:

Homework Statement


hey, I'm having issues with a problem, and my book doesn't seem to show me how to do it.
so,
i have a curve x = ky^2 and I'm to rotate it about the x-axis. I need to find the surface area generated.

How do i use the first theorem to do this? Thanks for the help

sorry i don't have a pic of the problem. but if you want to see here's a link to my book:
http://books.google.com/books?id=l-...&hl=en&sa=X&oi=book_result&resnum=1&ct=result

problem number 5.60
thanks once again

Homework Equations





The Attempt at a Solution

Welcome to Physics Forums.

Before we can help you, you need to show some effort in solving the problem yourself, either providing an attempted solution or at least detailing your thought.

Stating the theorem of Pappus and then seeing what you can do from there be a good start.
 
hey,

thanks for the welcome. I figured it out. It was just a bunch of math that I haven't done in the longest time. i had to figure out what k was which is where i messed up at the beginning. I used:
x = ky^2 and i just put b and a so...
a = kb^2 and found k to be b...which was wrong.

it was a system of equations cause there was a length to the object:

a + 15 = k(12.5)^2
a = k(7.5)^2
solving that i got k to be .15
so x = .15y^2

then applying the theorem:

A = 2(pi)(yL) = integral(2(pi)(yL), L, 0, b)

and solve that to get the answer.
Thanks for willing to help.
 

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