A circular arc whose radius is 24 cm makes an angle of 60° at the center. The perimeter of the sector formed is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 73.14 cm.
We know that,
The length of an arc(L) = 2πr × θ/360
L = 2 × 22/7 × 24 × 60/360
⇒ L = 44/7 × 24 × 1/6
⇒ L = 44/7 × 4
⇒ L = 176/7
⇒ L = 25.14 cm
Now,
The perimeter of the sector(P) = L + 2r
⇒ P = 25.14 + 2 × 24
⇒ P = 25.14 + 48
⇒ P = 73.14 cm
Thus, the perimeter of the sector is approximately 73.14 cm