Question

A chord of a circle of radius $6cm$ subtends a right angle at centre. The area of the minor segment $(\pi =3.14)$ is____.

• A. $9.82c{m}^2$
• B. $10.14c{m}^2$
• C. $10.26c{m}^2$
• D. $12.35c{m}^2$

Answer 1

The correct option is C $10.26c{m}^2$

$\text{Area of the minor segment}$ $=\text{Area}\left(SectorOACB\right)-\text{Area}\left(△AOB\right)$

$=\frac{{90}^{\circ }}{{360}^{\circ }}\times \pi \times r^2-\frac{1}{2}\times OA\times OB$

$=\frac{{90}^{\circ }}{{360}^{\circ }}\times 3.14\times 6^2-\frac{1}{2}\times 6\times 6$

$=28.26-18$

$=10.26{\text{cm}}^2$

Option C is correct.