An arc of a circle of radius 14cm subtends angle 300o at the center. Find the perimeter of the sector formed by the arc
Answer Details
To find the perimeter of the sector, we need to find the length of the arc and the length of the two radii that form the sector.
The circumference of a circle with radius 14cm is given by:
C = 2πr = 2π(14) = 28π
Therefore, the length of the arc subtending an angle of 300 degrees is:
L = (300/360) × 28π = 7π/3 × 28 ≈ 73.33cm
The length of the two radii that form the sector is:
2r = 2 × 14 = 28cm
Therefore, the perimeter of the sector is:
P = L + 2r ≈ 73.33 + 28 = 101.33cm
Hence, the correct option is (c) 101.33cm.