SSC CPO 2023 PYQ — Question 118

The correct answer is option 3 i.e. 27.

Given:

Perimeter of a sector of a circle is 24 cm 

Radius = 3 cm

Formula used:

Perimeter of a sector = (θ/360) × 2πr + 2r         ----- (1)

Area of the sector = (θ/360) × πr²              ---- (2)

Where r is the radius of the circle

Calculations:

According to the question;

⇒ 24 = 2r(1 + πθ/360)

⇒ πθ = 360 × 3         ----- (3)

Now using equation (3) in equation (2), we get

⇒ Area of the sector = [(360 × 3)/360] × 3²

⇒ 27