Mathematics • Year 8 • Unit 3 • Lesson 7

Circumference of Circles

Build fluency with C = πd and C = 2πr. One fully worked example, one guided example with blanks, then eight independent problems ramping from radius/diameter substitution to find-the-radius rearrangements.

Build · I Do / We Do / You Do

1. I do — fully worked example

Read every line. Each step has a short reason so you can see why, not just what.

Problem. A circle has radius r = 7 cm. Find the circumference. Give an exact answer and an approximation (use π ≈ 3.14159).

Step 1 — Identify what you're given.

r = 7 cm (radius given, not diameter).

Reason: knowing whether r or d is given decides which formula version to use.

Step 2 — Choose the formula (radius version).

C = 2πr

Reason: the 2 is essential — it converts radius into diameter (since d = 2r).

Step 3 — Substitute and simplify (exact form).

C = 2 × π × 7 = 14π cm (exact)

Reason: leaving π in the answer keeps it perfectly accurate. Useful when asked for an exact value.

Step 4 — Approximate (decimal form).

C ≈ 14 × 3.14159 ≈ 43.98 cm

Reason: most real-world questions want a decimal answer. Round only at the final step.

Answer: C = 14π ≈ 43.98 cm.

Stuck? Revisit lesson § Card 7 — when radius is given, use C = 2πr. The 2 is the most-forgotten part of the formula.

2. We do — fill in the missing steps

Same shape as Section 1, but this time diameter is given. Fill in each blank. 4 marks

Problem. A circular pond has diameter d = 15 m. Find the circumference. Give an exact answer and a decimal (2 d.p.).

Step 1 — Identify: diameter is given, so use the ______ version of the formula.

Step 2 — Write the formula:

C = π × ______

Step 3 — Substitute (exact form):

C = π × ______ = ______π m (exact)

Step 4 — Approximate to 2 d.p.:

C ≈ ______ × 3.14159 ≈ ______ m

Stuck? Revisit lesson § Card 6 — when diameter is given, use C = πd. No need to double anything.

3. You do — independent practice

Show all working. Use π ≈ 3.14 or the π button on your calculator. First three are foundation (clean radius/diameter). Middle three are standard (decimals, mixed). Last two are extension (find r or d from C).

Foundation — pick the right formula

3.1 r = 5 cm. Find C (2 d.p.). 1 mark

3.2 d = 20 cm. Find C (2 d.p.). 1 mark

3.3 r = 10 m. Find C in exact form (n π). 1 mark

Standard — decimals and mixed

3.4 r = 14 cm. Use π ≈ 22/7 to find C exactly (the 7 cancels nicely). 2 marks

3.5 d = 9.5 cm. Find C to 1 d.p. 2 marks

3.6 r = 0.6 m. Find C to 2 d.p. 2 marks

Extension — find r or d from C

3.7 C = 62.8 cm. Find the diameter d to the nearest cm. (Hint: rearrange C = πd → d = C ÷ π.) 2 marks

3.8 C = 44 cm. Use π ≈ 22/7 to find the radius r exactly. (Hint: r = C ÷ (2π).) 2 marks

Stuck on 3.7 / 3.8? Use the rearranged formulas from Card 8: d = C ÷ π and r = C ÷ (2π).

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Section 2 — We do (pond, d = 15)

Step 1: use the diameter version.
Step 2: C = π × d.
Step 3: C = π × 15 = 15π m (exact).
Step 4: C ≈ 15 × 3.14159 ≈ 47.12 m.

3.1 — r = 5 cm

C = 2π × 5 = 10π ≈ 31.42 cm.

3.2 — d = 20 cm

C = π × 20 = 20π ≈ 62.83 cm.

3.3 — r = 10 m (exact)

C = 2π × 10 = 20π m (exact). (≈ 62.83 m.)

3.4 — r = 14, π ≈ 22/7

C = 2 × (22/7) × 14 = 2 × 22 × 2 = 88 cm exactly.

3.5 — d = 9.5 cm

C = π × 9.5 ≈ 9.5 × 3.14159 ≈ 29.8 cm (1 d.p.).

3.6 — r = 0.6 m

C = 2π × 0.6 = 1.2π ≈ 1.2 × 3.14159 ≈ 3.77 m (2 d.p.).

3.7 — Find d from C = 62.8

d = C ÷ π = 62.8 ÷ 3.14159 ≈ 19.99 → d ≈ 20 cm.

3.8 — Find r from C = 44, π ≈ 22/7

r = C ÷ (2π) = 44 ÷ (2 × 22/7) = 44 ÷ (44/7) = 44 × (7/44) = 7 cm exactly. Check: 2 × (22/7) × 7 = 44 ✓.