Find the area of a sector with an arc length of 44 cm, which subtends a central angle of 30°.

Correct — D. Get the radius out of the arc first, then use the sector shortcut.

Arc = (θ⁄360) × 2πr
44 = (30⁄360) × 2 × 22⁄7 × r
44 = (1⁄12) × (44⁄7) × r = 44r⁄84
r = 84 cm

Area of a sector = ½ × arc × radius
= ½ × 44 × 84 = 1848 → option (d)

The options are printed in cm, but a sector area is in cm² — the paper's own slip, not yours.

Why the others are wrong

• (a)
  1584 cm — 1584 needs r = 72, since the area is ½ × 44 × r = 22r. A 72 cm radius gives a 30° arc of 2π × 72⁄12 = 37.7 cm, not the 44 cm the stem states.
• (b)
  1488 cm — 1488 ÷ 22 = 67.6…, not a whole radius at all. Every number here is built to come out exactly, so a radius that refuses to is a signal the formula has been mixed up.
• (c)
  1884 cm — 1884 is 1848 with the last two digits swapped — a transcription slip rather than a calculation. It would require r = 85.6…, which no 30° sector with a 44 cm arc has.

Two facts do all the work here.

Arc length = (θ⁄360) × 2πr — the share of the circumference the angle cuts off.
Sector area = (θ⁄360) × πr², which simplifies to ½ × arc × radius.

The second form is the one to carry. Once the arc and the radius are known the angle never appears again, and it is the circular twin of ½ × base × height.

At θ = 30° the sector is exactly one-twelfth of the circle, so its arc is one-twelfth of 2πr and its area one-twelfth of πr².

Key facts

• Arc length = (θ⁄360) × 2πr.
• Sector area = (θ⁄360) × πr², equal to ½ × arc × radius.
• A 30° sector is one-twelfth of the whole circle.
• Here r = 84 cm, so the area is ½ × 44 × 84 = 1848 cm².

Common traps

• Using ½ × arc × radius before finding the radius, and feeding the arc in as if it were r.
• Reading the 30° as the fraction 30⁄100 instead of 30⁄360.
• Taking π as 3.14, which turns the clean 84 into 84.08 and shakes your confidence in a correct answer.

No directly related past PYQ was found.