EASA / CAR Part-66 · Module 1 · 1.3 Geometry · Cat A

Circle: Area, Circumference & Sectors

Objective: everything about a circle follows from the radius. Change r and watch the circumference grow in proportion while the area grows with the square, then cut a sector and see what fraction of the whole you have taken.

The circle and its sector

How area and circumference grow with r

Radius r 4.0 m

Sector angle 90 °

Area

0m²

Circumference

Sector area

0m²

Arc length

A = πr² · C = 2πr = πd · sector = (θ/360) × πr²

Circumference is proportional to r, area is proportional to r². Double the radius and the circumference doubles, but the area quadruples. That difference catches people out constantly, and the graph beside the circle makes it visible: one line is straight, the other curves upward.

A sector is simply a fraction of the whole circle. The fraction is the angle over 360, so a 90° sector is a quarter of the area and a quarter of the circumference. The same fraction applies to both.

Diameter is twice the radius, so C = πd and C = 2πr are the same formula. Exam questions switch between the two deliberately; read carefully which one you have been given.

Try this: Set r = 2 m and note the area. Now set r = 4 m. Did the area double, or something else?
Try this: Set the sector to 90°. What fraction of the area is it, and does the arc length follow the same fraction?
Try this: Find the radius that makes the area and the circumference read the same number. Why is that not a coincidence?