In the given figure, the length of arc AB is equal to 3 times radius r of the circle.
Find the area of sector OAB in terms of radius r.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 1)

Answer 1

Formula used:

Area of an arc = θ/360 × πr² .

θ = arc / radius

1 radian = 180°/π

Calculation:

Here the arc = 3r

So, θ = 3r / r

⇒ 3^c

We know,

π^c = 180°

3^c = (180/π × 3) = 540/π degree

So, angle in degree (θ) = (540/π) degree

The area of the sector OAB is,

⇒ (540/π)/360 × πr²

⇒ 540/360 × r² = 3/2 r² = 1.5 r²

∴ The area of the sector OAB is 1.5 r².