quarter circle

Example 8 | Area bounded by arcs of quarter circles

Problem
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.

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724 Rectangle, semicircle, quarter-circle, and triangle | Centroid of Composite Area

723 Rectangle, quarter circle and triangle | Centroid of Composite Area

Problem 723
Locate the centroid of the shaded area in Fig. P-723.

722 Semicircle and quarter circle | Centroid of composite area

Problem 722
Locate the centroid of the shaded area in Fig. P-722 created by cutting a semicircle of diameter r from a quarter circle of radius r.

706 Centroid of quarter circle by integration

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

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Example 7 | Area inside the square not common to the quarter circles

Problem
The figure shown below is composed of arc of circles with centers at each corner of the square 20 cm by 20 cm. Find the area inside the square but outside the region commonly bounded by the quarter circles. The required area is shaded as shown in the figure below.