Find the area of the segment ACB, in a circle of radius 2.8 cm, if the angle subtended
by the chord AB at the centre is 60°.
Answers
Given:
✰ Radius of a circle = 2.8 cn
✰ Angle subtended by the chord AB at the centre = 60°
To find:
✠ The area of the segment ACB.
Solution:
Let's understand the concept first! First we will find the area of sector by using formula, then we will calculate area of traingle by using formula. After that we will substract area of traingle from area of sector to find area of segment.
In the circle, [ refer the attachment ]
O is the centre and,
- AO = BO = radius of circle = 2.8 cm
AB is a chord which subtents 60° angle at the centre O, i.e, ∠AOB = 60°
✭ Area of sector = θ/360° × πr² ✭
➛ Area of sector AOB = 60°/360° × 3.14 × (2.8)²
➛ Area of sector AOB = 1°/6° × 3.14 × 2.8 × 2.8
➛ Area of sector AOB = 1°/6° × 3.14 × 7.84
➛ Area of sector AOB = 4.10 cm²
✭ Area of triangle = 1/2 × b × h ✭
➛ Area of triangle AOB = 1/2 × 2.8 × 2.8
➛ Area of triangle AOB = 1/2 × 7.84
➛ Area of triangle AOB = 7.84/2
➛ Area of triangle AOB = 3.92 cm²
Now,
➣ Area of segment ACB = Area of sector AOB - Area of triangle AOB
➣ Area of segment ACB = 4.10 - 3.92
➣ Area of segment ACB = 0.18 cm²
∴ The area of the segment ACB = 0.18 cm²
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