Question

From each of the two opposite corners of a square of side $8$ cm, a quadrant of a circle of radius $1.4$ cm is cut. Another circle of radius $4.2$ cm is also cut from the centre as shown in Fig. Find the area of the remaining (shaded) portion of the square. (Use $\pi$ $=\frac{22}{7}$).

Answer 1

$\Rightarrow$ Here $a=8cm$

$\Rightarrow$ Area of square $=a^2=(8{)}^2=64c{m}^2$

$\Rightarrow$ Here radius of circle $R=4.2cm$

$\Rightarrow$ Area of of circle $=\pi R^2=\frac{22}{7}\times (4.2{)}^2$

$\therefore$ Area of of circle $=55.44c{m}^2$

$\Rightarrow$ Radius of sector $r=1.4cm$ and $\theta ={90}^o$

$\Rightarrow$ Area of $2$ sectors $=2\times \frac{\theta }{{360}^o}\pi r^2$

$\Rightarrow$ Area of $2$ sectors $=2\times \frac{{90}^o}{{360}^o}\times \frac{22}{7}\times (1.4{)}^2$

$\therefore$ Area of $2$ sectors $=3.08c{m}^2$

$\Rightarrow$ Area of shaded region = Area of square - ( Area of circle +Area of $2$ sectors)

$\Rightarrow$ Area of shaded region $=64-(55.44+3.08)$

$\therefore$ Area of shaded region $=64-58.52=5.48c{m}^2$