Question

Find the area of the segment of a circle whose radius is 10 cm and the angle subtended by
the corresponding chord at the centre is 30°.​

Answer 1

Step-by-step explanation:

The radius of the circle = 10 cm.

Chord PQ subtends an angle = 60 deg at the centre.

PQO is an equilateral triangle, O being the centre of the circle.

The segment PQO = 1/6 of the area of the circle = (1/6)(22/7)*10^2 = 52.38085238 sq cm.

Triangle POQ = [10^2*sin 60]/2 = 43.30127019 sq cm.

The minor sector = 52.38085238 - 43.30127019 = 9.07958219 sq cm.

The major sector = 6*52.38085238 - 9.07958219 = 305.2055321 sq cm.

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Answer 2

Answer:

The radius of the circle = 10 cm. Chord PQ subtends an angle = 60 deg at the centre. PQO is an equilateral triangle, O being the centre of the circle. The segment PQO = 1/6 of the area of the circle = (1/6)(22/7)*10^2 = 52.38085238 sq cm