The proportion of various sectors in a pie chart is directly proportional to

Start from the definition. A pie chart treats the full circle as 360 degrees, so each sector's share of the whole is its central angle divided by 360. The proportion is therefore directly proportional to the angle of the sector, which is option B.

Why the others are wrong:

• Perimeter (A): the perimeter of a sector is the arc length plus two radii. The arc scales with the angle, but the two radii add a fixed constant, so the perimeter is not proportional to the angle.
• Area (C): for a fixed radius, sector area does scale with the angle, since area equals (θ/360) × πr². However, the question asks what the chart's proportion is directly proportional to, and a pie chart is drawn and read by angle. Area works only as a secondary effect of equal radii.
• D: incorrect, because B is correct.

Core concept: sector geometry and graphical representation of data. This connects to data interpretation skills useful in Mains answers that use charts and statistics, where reading the right quantity matters.

Trap: aspirants pick area because it also varies with the angle. Remember that the question asks for the quantity the chart itself encodes.