SOLUTION: Two semicircles are placed in a rectangle. The width of the rectangle is 9ft. Find the area of the shaded region. Use the value 3.14 for pi. Do not round!

Algebra ->  Rectangles -> SOLUTION: Two semicircles are placed in a rectangle. The width of the rectangle is 9ft. Find the area of the shaded region. Use the value 3.14 for pi. Do not round!      Log On


   



Question 550970: Two semicircles are placed in a rectangle. The width of the rectangle is 9ft. Find the area of the shaded region. Use the value 3.14 for pi. Do not round!
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 
I assume the figure is like this



And the shaded area is this apple core: 



The rectangle is a square with side 9, so its area is 9² or 81 sq.ft.

The two semicircles make 1 complete circle, with diameter 9, which
means its radius is 9%2F2 and the area is pr²
or p%289%2F2%29%5E2 or 81%2F4p.

So if we subtract the circle's area from the square's area, we get

81 - 81%2F4p =

81 - 81%2F4×3.14

81 - 20.25×3.14

81 - 63.585

17.415 sq.ft.

Edwin