Question

Four equal circles each of radius 5 cm touch each other as shown in the given figure Find the area between the circles (Use $\pi =3.14$)

• A. 15.5 $c{m}^2$
• B. 21.5 $c{m}^2$
• C. 18.5 $c{m}^2$
• D. 22.5 $c{m}^2$

Answer 1

The correct option is B 21.5 $c{m}^2$

Side of square $ABCD=5cm+5cm=10cm$
Area of square $ABCD=10\times 10=100c{m}^2$
Area of one sector
$=\frac{\theta }{{360}^{\circ }}\times \pi r^2=\frac{{90}^{\circ }}{{360}^{\circ }}\times 3.14\times {\left(5\right)}^{2}c{m}^2$
$=\frac{1}{4}\times 3.14\times 25c{m}^2$
Area of four sectors
$4\times \frac{1}{4}\times 3.14\times 25c{m}^2=78.50c{m}^2$
The area between the circles
$=$ Area of square ABCD -Area of four sector
$(100-78.5)c{m}^2=21.5c{m}^2$