A circular arc whose radius is 12 cm makes an angle of 30° at the centre. Find the perimeter (in cm) of the sector formed. (Use π = 3.14)

Question

Accepted Answer

The perimeter of a sector is the sum of the lengths of the two radii and the arc length.

Given:  
Radius (r) = 12 cm  
Central angle (θ) = 30°  
π = 3.14

Step 1: Calculate the arc length (L).  
Arc length formula: L = (θ/360) × 2πr  
L = (30/360) × 2 × 3.14 × 12  
L = (1/12) × 2 × 3.14 × 12  
L = 2 × 3.14 = 6.28 cm

Step 2: Calculate the perimeter of the sector.  
Perimeter = 2 × radius + arc length  
Perimeter = 2 × 12 + 6.28 = 24 + 6.28 = 30.28 cm

Rechecking the calculation shows the perimeter is 30.28 cm, which corresponds to option 2.

Answer

Answer

Answer