ARC — Arc Length and Athletics Track | Chapter 6

DISCOVER

Start with a question.

If the angle at the centre is one quarter of a full turn, what fraction of the circumference is the arc?

An arc subtending θ degrees has θ/360 of the full circumference. On a stadium-shaped track the extra distance in outer lanes comes from the bends.

l = \frac{θ}{360} \times 2 πr

Arc length is not sector perimeter. A one-lap stagger is not automatically the total stagger for every race format.

Central angle (degrees): 90

The bold curve is an arc; the two straight radii are not part of its length.

Compare one complete circuit on two running lines. The straight portions have equal lengths.

Lane width (m): 1.22

Model first-lane 0.30 m and next-lane 0.20 m measurement offsets

Schematic running lines, not an official track specification. Measurement offsets affect the first-to-second lane difference.

Use the central angle. Find its fraction of 360°. Multiply by circumference. Add straight edges only when a whole boundary is requested.

Radius 3.5 cm; central angle 60°. Exercise 6.1 Q3(i) requests π ≈ $\frac{22}{7}$ .

Find the arc length.

l = (θ/360) × 2πr.

About 3.67 cm (no final decimal-place requirement is stated in Q3).

A — Attempt independently. Make a prediction or start a sketch.
I — Investigate the idea. Identify the boundary, region and given conditions.
M — Make connections. Relate the figure to a known property or rearrangement.
S — Scrutinise your reasoning. Check conditions, units and whether the result is exact.

Think first. Use AI purposefully. Verify always.

A 90° sector has radius 4 cm. Give the exact arc length and exact sector perimeter.

Your reasoning

Why do equal straight sections not contribute to the difference between two running-line lengths?

Explain your conclusion

Textbook connection: Ganita Manjari · Grade 9 · Part I · Chapter 6 · 6.4 · Figures 6.8–6.11 · printed pages 125–127.