**Areas related to Circles ncert solutions Chapter 12 Exercise 12.3 Question 5**

**5.** From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the diagram. Find the area of the remaining portion of the square.

**Solution:**

Diameter of inner circle = 2 cm

Therefore, its radius =r1= **cm**

And, radius of quadrant of circle cut at each corner of the square = r=1 cm

**Area of shaded portion = Area of square - Area of four equal Quadrants of circle-Area of inner circle (1)**

Area of square = side x side =4 x 4=16 **(2)**

which is angle of sector cut at the corner of the square.

**{ABCD is a square}**

Area of one quadrant of circle cut at one corner of the square = where, r is the radius of circle and is the angle of sector.

Area of one quadrant of circle cut at one corner of the square

Therefore, Area of four Quadrants of circle cut at each corner of the square

**(3)**

**Area of inner circle** **(4)**

Putting **(2)**, **(3)** and **(4)** in **(1)**, we get

**Area of shaded portion**