Circles: circumference & π

A circle's key measurements are the radius (from the centre to the edge) and the diameter (all the way across through the centre, which is always twice the radius). π (pi) is a special number, approximately 3.14, that describes the fixed relationship between a circle's circumference (the distance around it) and its diameter — no matter the circle's size, circumference ÷ diameter always equals π. This gives the formula: circumference = π × diameter, or equivalently, circumference = 2 × π × radius.

Key terms

Radius:

The distance from the centre of a circle to its edge.

Diameter:

The distance across a circle through its centre (twice the radius).

Circumference:

The distance around the edge of a circle.

Pi (π):

The fixed ratio of a circle's circumference to its diameter, approximately 3.14.

Questions

1. 1. The radius of a circle is:

   • The distance around it
   • The distance from the centre to the edge
   • The distance across through the centre
   • The area

2. 2. The diameter of a circle is:

   • Half the radius
   • The same as the radius
   • Twice the radius
   • The circumference

3. 3. The circumference is:

   • The distance across a circle
   • The distance around a circle
   • The centre point
   • The radius

4. 4. π (pi) is approximately:

   • 1.14
   • 2.14
   • 3.14
   • 4.14

5. 5. If the radius is 5cm, the diameter is:

   • 2.5cm
   • 5cm
   • 10cm
   • 25cm

6. 6. If the diameter is 12cm, the radius is:

   • 3cm
   • 6cm
   • 12cm
   • 24cm

7. 7. The formula for circumference using diameter is:

   • C = π + d
   • C = π × d
   • C = π - d
   • C = π ÷ d

8. 8. A circle has a diameter of 4cm. What is its circumference (using π ≈ 3.14)?

   • 4cm
   • 8cm
   • 12.56cm
   • 16cm

9. 9. A circle has a radius of 3cm. What is its circumference (using π ≈ 3.14)?

   • 9.42cm
   • 18.84cm
   • 6cm
   • 3.14cm

10. 10. A circle has a diameter of 10cm. What is its circumference (using π ≈ 3.14)?

    • 10cm
    • 15.7cm
    • 31.4cm
    • 62.8cm

11. 11. Circumference ÷ diameter always equals:

    • 1
    • 2
    • π
    • 0

12. 12. A circular table has a radius of 0.5m. What is its circumference (using π ≈ 3.14)?

    • 1.57m
    • 3.14m
    • 0.785m
    • 6.28m

13. 13. Which formula correctly uses radius instead of diameter?

    • C = π × r
    • C = 2 × π × r
    • C = π ÷ r
    • C = π + r

14. 14. A bicycle wheel has a diameter of 0.7m. Approximately how far does it travel in one full rotation (using π ≈ 3.14)?

    • 0.7m
    • 1.4m
    • 2.2m
    • 4.4m

15. 15. A circular garden bed has a circumference of 31.4m. What is its diameter (using π ≈ 3.14)?

    • 5m
    • 10m
    • 15.7m
    • 20m

16. 16. A circular pool has a circumference of 18.84m. What is its radius (using π ≈ 3.14)?

    • 3m
    • 6m
    • 9m
    • 12m

17. 17. A wheel with radius 0.35m makes 10 full rotations. How far does it travel in total (using π ≈ 3.14)?

    • 2.2m
    • 10m
    • 21.98m
    • 35m

18. 18. Two circles have diameters of 4cm and 8cm. How does the circumference of the bigger circle compare to the smaller one?

    • Same
    • Twice as big
    • Four times as big
    • Half as big

19. 19. A running track's inner circle has a radius of 40m. Approximately how far is one full lap around it (using π ≈ 3.14)?

    • 125.6m
    • 251.2m
    • 502.4m
    • 40m

20. 20. Why does circumference ÷ diameter always give the same value (π) no matter the circle's size?

    • It's a coincidence that only works for small circles
    • It's a fixed mathematical property true for every circle
    • It only works for circles with whole-number radii
    • It changes depending on units used