GANITA MANJARI · GRADE 9 · PART I · CHAPTER 6
DISCOVER — Circumference and π
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a question.
Compare circles of different sizes. Does circumference divided by diameter change?
Say what you expect to stay the same and what you expect to change. Then test your prediction in the visual below.
Understand
All circles share the ratio = π. Diameter is twice radius. Physical measurements estimate this ratio; they do not give its exact value.
Key Ideas
Using πr for a full circumference loses a factor of 2. The radius is not the diameter.
Visualise
Change the diameter. Predict what happens to circumference and their ratio.
C ≈ 18.8496 units; for every circle.
Method
Identify radius or diameter. Convert d = 2r if needed. Keep π in an exact answer unless an approximation is requested.
Worked Example
Given
A circle has radius 5 cm.
To Find
Find its exact circumference.
Formula / Property / Theorem / Reasoning
C = 2πr.
Solution
- The diameter is 10 cm.
- C = π × 10 cm.
Result
10π cm. Original AIMS example.
AIMS Method
- 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.
Focused Practice
A circle has diameter 14 cm. Give its exact circumference, then estimate using π ≈ .
Check & Feedback
A circle doubles in diameter. What happens to ?
Textbook connection: Ganita Manjari · Grade 9 · Part I · Chapter 6 · 6.2 · Figures 6.5–6.7 · printed pages 120–122.