Question

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

Answer 1

Answer:

See below

Step-by-step 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:

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