The proportion of various items in a pie diagram is directly proportional to the

The correct answer is B) Angle of slices. In a pie diagram the whole circle stands for 360 degrees, and each item gets a sector whose central angle is (value / total) x 360. So the angle at the centre is what carries the proportion.

• A) Area of slices: The area of a sector is also proportional to its angle, so area moves in step with the proportion. But the direct, constructible link is the angle. Area is a consequence of the angle, not the variable you set when drawing the chart, and it is hard to judge by eye.
• C) Length of curved arcs: Arc length is proportional to the angle only when the radius is fixed. It is not the defining quantity, so it is not the answer.
• D) Perimeter of slices: The perimeter includes the two straight radii, which are the same for every slice of a given circle. It does not vary in proportion to the value, so this is wrong.

Core concept: constructing a pie chart from percentages, using angle = percentage of 360 degrees. This links to data representation in Statistics and to Mains questions on reading graphical data in government reports.

Trap: picking Area because sector area is also proportional to the angle. Remember what the question asks: the quantity directly set by the data when you draw the chart.