# circular quadrant

## 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.

## 04 Four overlapping semi-circles inside a square

## 03 Area enclosed by pairs of overlapping quarter circles

**Example 03**

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.

## 02 Area bounded by arcs of quarter circles

**Example 02**

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.

## 01 Arcs of quarter circles

**Example 01**

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.

## 24-25 Largest rectangle inscribed in a circular quadrant

**Problem 24**

Find the area of the largest rectangle that can be cut from a circular quadrant as in Fig. 76.

## 53 - 55 Solved Problems in Maxima and Minima

**Problem 53**

Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.