Circumference and Perimeter Practice

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Chapter 5 Measurement — Example & Part 1: Circumference (to 2 decimal places)

Worked example: Find the circumference of a circle with radius 7 cm. Show your method.

Use C = 2πr or C = πd. Calculation: C = 2 × π × 7 = 14π ≈ 43.98 cm (to 2 d.p.).

1. Find the circumference of a circle with radius 4 cm. Give your answer to two decimal places.

2. Find the circumference of a circle with diameter 10 cm. Give your answer to two decimal places.

3. Find the circumference of a circle with radius 2.5 m. Give your answer to two decimal places. (Write units.)

4. Find the circumference of a circle with diameter 15 cm. Give your answer to two decimal places.

5. Concept check: Which formula gives the circumference when you know the diameter?

C = 2πr

C = πd

C = πr²

✏️ Part 2: Perimeter of Sectors & Composite Shapes

6. A sector of a circle has radius 8 cm and a central angle of 60°. Find the perimeter of the sector. Give your answer to two decimal places.

Hint: Perimeter = 2 × radius + arc length. Arc length = (θ/360) × 2πr.

7. A garden bed is made from a rectangle 6.0 m wide and 2.0 m tall, with a semicircle attached to one 6.0 m side (the semicircle has diameter 6.0 m). Find the perimeter of the garden bed (the length around the outside). Give your answer to two decimal places. Include units.

8. Find the perimeter of this shape: a quarter-circle of radius 4 cm attached to two straight sides that meet at right angles (i.e. the boundary is the two straight radii plus the arc). Give your answer to two decimal places.

9. Challenge: A sector has radius 12 cm and its arc length is 8π cm. What is the central angle of the sector? Then find the sector's perimeter (to two decimal places).