Hi!

Problem is to find the area. (See picture below, along with description of problem).

The book says, $\displaystyle A=2\pi\cdot \bar{x}\cdot L $ , where $\displaystyle \bar{x}$ 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: $\displaystyle 2\pi\cdot \left(\underbrace{100-\frac{50\cdot sin(\frac{\pi}{4})}{\frac{\pi}{4}}\cdot cos(\frac{\pi}{4})}_{\text{x-coordinate}}\right)\cdot \underbrace{\frac{2\pi\cdot 50}{4}}_{\text{Length of 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 $\displaystyle 9.87(10^{4}) $

Thx!