Question

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 Fig.Find the area of the remaining portion of the square.

• A. $\frac{36}{7}c{m}^2$
• B. $\frac{68}{9}c{m}^2$
• C. $\frac{58}{7}c{m}^2$
• D. $\frac{68}{7}c{m}^2$

Answer 1

The correct option is D

$\frac{68}{7}c{m}^2$

Side of the square = 4 cm
Radius of the circle = 1 cm
Four quadrant of a circle are cut from corner and one circle of radius is cut from middle.
Area of square $=(side{)}^2=4^2=16c{m}^2$
Area of the quadrant $=\frac{\left(\pi R^2\right)}{4}c{m}^2=\frac{(\frac{22}{7}\times 1^2)}{4}=\frac{11}{14}c{m}^2$
$\therefore$ Total area of the 4 quadrants $=4\times \left(\frac{11}{14}\right)c{m}^2=\frac{22}{7}c{m}^2$

Area of the circle $=\pi R^{2}c{m}^2=(\frac{22}{7}\times 1^2)=\frac{22}{7}c{m}^2$
Area of the shaded region = Area of square - (Area of the 4 quadrants + Area of the circle)
$=16c{m}^2-(\frac{22}{7}+\frac{22}{7})c{m}^2$
$=\frac{68}{7}c{m}^2$