A circular arc makes an angle of 15° at the centre. If the radius of the circular arc is 14 cm, what is the perimeter (correct up to two decimal places) of the sector so formed? (π = 3.14)

Question

Accepted Answer

Step 1: Given the radius r = 14 cm and the central angle θ = 15°.

Step 2: Calculate the length of the arc (L) using the formula:
L = (θ/360) × 2πr
= (15/360) × 2 × 3.14 × 14
= (1/24) × 2 × 3.14 × 14
= (1/24) × 87.92
= 3.6633 cm (approx)

Step 3: The perimeter of the sector is the sum of the arc length and the two radii:
Perimeter = L + 2r
= 3.6633 + 2 × 14
= 3.6633 + 28
= 31.6633 cm

Step 4: Round to two decimal places:
Perimeter ≈ 31.66 cm

Note: The answer choices provided include 31.66 cm and 35.32 cm. Rechecking the arc length calculation:

L = (15/360) × 2 × 3.14 × 14 = (1/24) × 87.92 = 3.6633 cm

Perimeter = 3.6633 + 28 = 31.6633 cm ≈ 31.66 cm

Therefore, the correct perimeter is 31.66 cm, which corresponds to option 4.

Answer

Answer

Answer