Question

A chord of a circle of radius $10cm$ subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use $\pi =3.14$)

Answer 1

(i) Area of minor segment (shaded region) $=$ Area of the quadrant $AOB-$ Area of the $△AOB$

$=\frac{1}{4}\times \pi r^2-\frac{1}{2}\times AO\times OB$

$=\frac{1}{4}\times 3.14\times {\left(10cm\right)}^2-\frac{1}{2}\times 10cm\times 10cm$

$=\frac{1}{4}\times 3.14\times 100{cm}^2-50{cm}^2$

$=78.5{cm}^2-50{cm}^2$

$=28.5{cm}^2$

(ii) Area of the major segment $=$ Area of the circle $-$ Area of the minor segment

$=\pi r^2-28.5{cm}^2$

$=3.14\times {\left(10cm\right)}^2-28.5{cm}^2$

$=314{cm}^2-28.5{cm}^2$

$=285.5{cm}^2$