A circular are whose radius is 4 cm makes an angle 45° at the centre. Find the perimeter of the sector formed.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. .
r = 4cm
θ = 45º
the length of an arc is L= 2πr × θ/360º
⇒ L = 2π × 4 × 45/360 = 8π × 1/8 = πcm
The perimeter of the sector is the sum of the arc length and the two radii.
Thus:
⇒ Perimeter = L + 2r
⇒ Perimeter = π + 2 × 4 = π + 8 cm
⇒ Perimeter = 22/7 + 8 = (22 + 56)/7 = 78/7 cm