Question

A chord of a circle of radius 10cm.substends a right angle at the center. Find the area of the corresponding

Answer 1

Question:

A chord of a circle of radius 10cm.substends a right angle at the center. Find the area of the corresponding?

Answer:

Radius = 10 cm

Major segment = 360° - 90° = 270°

Area of the sector = 270°

= (270°/360°) × π r2 cm2

= (3/4) × 102π = 75 π cm2

= 75 × 3.14 cm2 (Put the value of π = 3.14)

= 235.5 cm2

Height of ΔAOB = OA = 10 cm
Base of ΔAOB = OB = 10 cm

Area of ΔAOB

= 1/2 × OA × OB

= 1/2 ×10 × 10

= 50 cm2

Major segment = 90°

Area of the sector = 90°

= (90°/360°) × π r2 cm2

= (1/4) × 102π = 25 π cm2

= 25 × 3.14 cm2

= 78.5 cm2

Area of the minor segment = Area of the sector making angle 90° - Area of ΔAOB

= 78.5 cm2 - 50 cm2

= 28.5 cm2

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