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)?

Correct — D. The perimeter of a sector is the arc plus both radii, because the sector is bounded by two straight edges and one curve.

Arc length = (θ⁄360) × 2πr
= (15⁄360) × 2 × 3.14 × 14
= (1⁄24) × 87.92 = 3.6633… ≈ 3.66 cm

Add the two radii:
3.6633 + 28 = 31.6633 ≈ 31.66 cm → option (d).

Why the others are wrong

• (a)
  21.32 cm — 21.32 doubles the arc and adds a single radius (3.66 + 3.66 + 14). It is the radius that repeats, not the arc.
• (b)
  17.66 cm — 17.66 adds only one radius: 3.66 + 14. A sector has two straight edges, so both radii belong in its perimeter.
• (c)
  35.32 cm — 35.32 counts the arc twice (3.66 + 3.66 + 28). The boundary carries one arc and two radii, not two arcs and two radii.

A sector is bounded by three edges — two radii and one arc.

Perimeter = 2r + (θ⁄360) × 2πr. The fraction θ⁄360 is the share of the whole circle the angle cuts out, so a 15° arc is one twenty-fourth of the circumference.

At small angles the straight edges dominate: here 28 cm of the 31.66 cm total is radius and only 3.66 cm is curve. That is why forgetting one radius costs you 14 cm of the 31.66 cm.

Key facts

• Perimeter of a sector = 2r + (θ⁄360) × 2πr.
• A 15° arc is one twenty-fourth of the circumference.
• With r = 14 and π = 3.14 the circumference is 87.92 cm.

Common traps

• Answering the arc length alone or adding just one radius
• Switching to π = 22⁄7 when the paper prints 3.14

No directly related past PYQ was found.