These articles may help you:
Surface of Revolution -- from Wolfram MathWorld
Pappus's Centroid Theorem -- from Wolfram MathWorld
However, answer to your problem is
Hi!
Problem is to find the area. (See picture below, along with description of problem).
The book says, , where is the y-coordinate of the centroid of the line. And L is the length of the line.
I donīt get correct results :/
I did for the A circular arc:
Then I did the same for the B arc. And I add them.
The result is incorrect. Even if I try to add the top area as well, I get the wrong result.
Note: Instead of 2 inch use 50mm , and the answer should be
Thx!
These articles may help you:
Surface of Revolution -- from Wolfram MathWorld
Pappus's Centroid Theorem -- from Wolfram MathWorld
However, answer to your problem is
I'd first calculate it the regular way using the formula:
Right?
Me, I'd use complex coordinates. The equation for the top curve is . You can do the bottom one. Thus, the parametric form of the top curve is . Now, just substitute both expressions, making sure you get the starting and ending t times correctly, into the formula above.
After I get the right answer, then I'd go on to calculate the moment of the figure and then the y-coordinate of the centroid and see if I get agreement.