Question

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

Answer 1

Area of shaded region $=$ Area of square $ABCD$ $-$ Area of 4 quadrants $-$ Area of circle with diameter $2$ cm
Area of square $=4\times 4=16c{m}^2$

Area of sector $=\frac{\theta }{360}\times \pi \times r^2$

Area of 4 quadrants $=4\times \frac{90}{360}\times \pi \times 1\times 1$
$=3.14c{m}^2$
Area of circle$=\pi \times r^2$ $=\pi \times 1\times 1$
$=3.14c{m}^2$
$\therefore$ Area of shaded region $=16-6.28$ $=9.72c{m}^2$