How to Draw a Sector with Arc of Angular Measure 60°

Required: Compass, ruler, protractor, pencil.

Step 1: Draw a circle. Use a compass. Mark the centre as O. Choose a suitable radius (e.g., 5 cm).

Step 2: Draw the first radius. Draw a straight line from O to any point A on the circle. This is radius OA.

Step 3: Measure 60° using protractor. Place the protractor at O with the baseline along OA. Mark a point at 60° on the protractor scale.

Step 4: Draw the second radius. Join O to the 60° mark — extending it to cut the circle at B. This is radius OB.

Step 5: Mark the arc. The arc AB (the shorter arc, inside the 60° angle) is the bounding arc of the sector.

Step 6: Shade the sector. Shade the region bounded by OA, OB, and arc AB.

Result: The shaded region AOB is a sector with central angle (angular measure) = 60°.

For a circle of radius r, a sector with central angle θ = 60°:

Arc length: l = (θ/360°) × 2πr = (60/360) × 2πr = (1/6) × 2πr = πr/3

Area of sector: A = (θ/360°) × πr² = (60/360) × πr² = πr²/6

Example — radius = 6 cm, θ = 60°: Arc length = π × 6 / 3 = 2π ≈ 6.28 cm Area = π × 36 / 6 = 6π ≈ 18.85 cm²

Note: A 60° sector is exactly 1/6 of the full circle. (Since 60/360 = 1/6)

Sector: The 'pie slice' region of a circle bounded by two radii and an arc.

Minor sector: The smaller sector (central angle < 180°). The 60° sector is a minor sector.

Major sector: The larger sector (central angle > 180°). The remaining 300° region would be the major sector.

Central angle (Angular measure): The angle at the centre O between the two radii. Here = 60°.

Arc: The curved part of the sector boundary — here it is 1/6 of the circumference.

Relationship: • Sum of minor and major central angles = 360° • Here: 60° + 300° = 360°

Special sectors: • 90° sector = quarter circle (1/4) • 120° sector = one-third circle (1/3) • 60° sector = one-sixth circle (1/6) • 180° sector = semicircle (1/2)