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

Given : from a square of side 8 cm form quadrants from each corner are cut of radius 1.4 cm also a circle from centre of diameter 4.2 cm is cut

$\Rightarrow$ Radius of circle in the centre = $\frac{Diameter}{2}$ = $\frac{4.2}{2}$ = 2.1 cm

Now area of square = $(8cm{)}^2$ = $64c{m}^2$ ..... (i)

Area of each quadrant = $\frac{1}{4}\pi (1.4cm{)}^2$ ------(ii)

Area of 4 quadrant = 4 $\times$ $\frac{1}{4}\pi (1.4cm{)}^2$

= $\pi$ $\times$ 1.4 $\times$ 1.4 $c{m}^2$

= 6.16 $c{m}^2$

Also area of circle = $\pi$ $\times$ $(2.1cm{)}^2$

=13.86 $c{m}^2$

Hence area of remaining portion = Area of square – (area of 4 quadrants + area of circle)

= 64 $c{m}^2$ – 16.16 $c{m}^2$ + 13.86 $c{m}^2$

= 64 $c{m}^2$ – 20.02 $c{m}^2$

= 43.98 $c{m}^2$