Question

what is the area of a minor sector if the radios
is 3.5

Answer 1

Answer:

Radius of the circle = 3.5 cm

ΔAOB is isosceles as two sides are equal.

∴ ∠A = ∠B

Sum of all angles of triangle = 180°

∠A + ∠B + ∠C = 180°

⇒ 2 ∠A = 180° - 60°

⇒ ∠A = 120°/2

⇒ ∠A = 60°

Triangle is equilateral as ∠A = ∠B = ∠C = 60°

∴ OA = OB = AB =3.5 cm

Area of equilateral ΔAOB = √3/4 × (OA)2 = √3/4 ×3.52

= (12.25√3)/4 cm2 = 5.304 cm2

Angle subtend at the centre by minor segment = 30°

Area of Minor sector making angle 30° = (30°/360°) × π r2 cm2

= (1/12) × 3.52 π cm2 = 12.25/12 π cm2

= 1.020× 3.14 cm2 = 3.205 cm2