Mathematics • Year 8 • Unit 3 • Lesson 8
Area of Circles
Build fluency with A = πr². One fully worked example, one guided example with blanks, then eight independent problems ramping from clean radii to diameter conversions and semicircles.
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 = 5 cm. Find the area. Give an exact answer and an approximation (use π ≈ 3.14159).
Step 1 — Identify the radius.
r = 5 cm.
Reason: the area formula uses the radius. If diameter were given, you'd halve it first.
Step 2 — Write the formula.
A = π × r²
Reason: this is the area formula. The r is squared, not π.
Step 3 — Square the radius first.
r² = 5² = 25
Reason: order of operations — square before multiplying by π.
Step 4 — Multiply by π.
A = π × 25 = 25π cm² (exact)
Reason: leaving π in keeps the answer perfectly accurate.
Step 5 — Approximate and add units.
A ≈ 25 × 3.14159 ≈ 78.54 cm²
Reason: area is in square units (cm²), never linear units.
Answer: A = 25π ≈ 78.54 cm².
2. We do — fill in the missing steps
Same shape as Section 1, but this time diameter is given. You must halve it first. Fill in each blank. 4 marks
Problem. A circle has diameter d = 14 cm. Find the area. Use π ≈ 22/7 (the 7 cancels cleanly).
Step 1 — Convert diameter to radius:
r = d ÷ 2 = 14 ÷ 2 = ______ cm
Step 2 — Write the formula:
A = π × r²
Step 3 — Square the radius:
r² = ______² = ______
Step 4 — Multiply by π (use 22/7):
A = (22/7) × ______ = ______ cm²
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). Middle three are standard (diameter or decimals). Last two are extension (semicircles and find-the-radius).
Foundation — radius given
3.1 r = 3 cm. Find A to 2 d.p. 1 mark
3.2 r = 8 cm. Find A in exact form (n π). 1 mark
3.3 r = 10 m. Find A to 2 d.p. 1 mark
Standard — diameter or decimals
3.4 d = 10 cm. Find A to 2 d.p. (Hint: halve to find r first.) 2 marks
3.5 r = 7 cm. Use π ≈ 22/7 to find A exactly. 2 marks
3.6 r = 2.5 m. Find A to 2 d.p. 2 marks
Extension — semicircles & find the radius
3.7 A semicircle has radius r = 6 cm. Find its area to 2 d.p. (Hint: semicircle area = ½ × π × r².) 2 marks
3.8 A circle has area A = 200 cm². Find the radius r to the nearest cm. (Hint: r = √(A ÷ π).) 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (d = 14, π ≈ 22/7)
Step 1: r = 14 ÷ 2 = 7 cm.
Step 3: r² = 7² = 49.
Step 4: A = (22/7) × 49 = 22 × 7 = 154 cm² (exact).
3.1 — r = 3 cm
A = π × 3² = 9π ≈ 28.27 cm².
3.2 — r = 8 cm (exact)
A = π × 8² = 64π cm² (exact). (≈ 201.06 cm².)
3.3 — r = 10 m
A = π × 10² = 100π ≈ 314.16 m².
3.4 — d = 10 cm
r = 10 ÷ 2 = 5 cm. A = π × 5² = 25π ≈ 78.54 cm².
3.5 — r = 7, π ≈ 22/7
A = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm² exactly.
3.6 — r = 2.5 m
A = π × 2.5² = π × 6.25 ≈ 19.63 m².
3.7 — Semicircle r = 6
A = ½ × π × 6² = ½ × 36π = 18π ≈ 56.55 cm².
3.8 — Find r from A = 200
r² = A ÷ π = 200 ÷ 3.14159 ≈ 63.66. r = √63.66 ≈ 7.98 → r ≈ 8 cm (to nearest cm). Check: π × 8² = 64π ≈ 201.06 cm² ≈ 200 ✓.