Question

I don't know the answer please tell me the correct one​

Answer 1

See below

Explanation:

Radius (r) = 8 inches

Chord = 8 inches

Since, length of radii and chord are equal. Thus the Triangle so formed by radii and chord will be an equilateral triangle.

`\implies` angle subtended at the centre of the circle
`(\theta)=60\degree`

Formula for area of segment of a circle is given as:

`A = \frac{ {r}^(2) \theta }{36 0 \degree} \pi - (1)/(2) {r}^(2) \sin \theta \\ \\ \implies \: A = \frac{ {(8)}^(2) ( \cancel{60 \degree)}}{ \cancel{360 \degree}} \pi - (1)/(2) {(8)}^(2) \sin 60\degree \\ \\ \implies \: A = \frac {64 }{6} \pi - (1)/(2) * 64 * ( √(3) )/(2) \\ \\ \implies \: \huge \purple{ \boxed{A = \bigg( \frac {32 }{3} \pi - 16 √(3)\bigg) }\: sq\:in}`