circular quadrant

Problem 706
Determine the centroid of the quarter circle shown in Fig. P-706 whose radius is r.
 

Example
The figure shown below consists of arcs of four semi-circles with centers at the midpoints of the sides of a square. The square measures 20 cm by 20 cm. Find the area bounded by these circular arcs shaded in the figure shown.
 

Example
The shaded regions in the figure below are areas bounded by two circular arcs. The arcs have center at the corners of the square and radii equal to the length of the sides. Calculate the area of the shaded region.
 

Example
Arcs of quarter circles are drawn inside the square. The center of each circle is at each corner of the square. If the radius of each arc is equal to 20 cm and the sides of the square are also 20 cm. Find the area common to the four circular quadrants. See figure below.
 

Example
The figure shown below are circular arcs with center at each corner of the square and radius equal to the side of the square. It is desired to find the area enclosed by these arcs. Determine the area of the shaded region.