The area of the given circle is 367 . It has been divided into six equal parts. The length of arc PQ will be

The correct answer is D, 2π.

The area is read as 36π, the intended form of this question. Area = πr², so πr² = 36π, giving r = 6 units. The circumference is 2πr = 12π.

Six equal parts means each sector subtends 360°/6 = 60° at the centre. Arc length = (θ/360) × 2πr = (60/360) × 12π = 2π.

• Option A, π, corresponds to a 30° angle, which is one-twelfth of the circle, not one-sixth.
• Option B, 3π, corresponds to 90°, a quarter circle, which fits four equal parts, not six.
• Option C, 4π, corresponds to 120°, a third of the circle, which fits three equal parts.

Core concept: arc length is the fraction of the circumference given by the central angle over 360°. The same logic carries into sector area and angle-based mensuration problems, which appear regularly in PCS quantitative aptitude.

Trap: students often use the full circumference or the sector area in place of the arc length, or they divide the area by six and then mix up the radius with the arc.