Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown.
Level 1 · Warm-up
1 A circle has diameter 7 cm. Circumference to 1 dp, in cm? (π ≈ 3.142)
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C = 3.142 × 7 = 22.0 cm.
2 A circle has radius 4 cm. Circumference to 1 dp, in cm? (π ≈ 3.142)
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C = 2 × 3.142 × 4 = 25.1 cm.
3 A circle has radius 6 cm. What is its diameter, in cm?
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d = 2r = 12 cm.
Level 2 · Core
4 What fraction of a circle is a 90° sector? (as a fraction)
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90/360 = 1/4.
5 Find the arc length of a 180° arc on a circle of radius 10 cm, to 1 dp. (π ≈ 3.142)
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½ × 2 × 3.142 × 10 = 31.4 cm.
6 A circle has radius 7 cm. Give its circumference in terms of π. (in terms of π)
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2 × 7 = 14, so C = 14π cm.
Level 3 · Challenge
7 A circle has circumference 44 cm. Find its diameter to 1 dp, in cm. (π ≈ 3.142)
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d = 44 ÷ 3.142 = 14.0 cm.
8 A 60° sector has radius 12 cm. Find its PERIMETER to 1 dp, in cm. (π ≈ 3.142)
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Arc = ⅙ × 2 × 3.142 × 12 = 12.6; plus 12 + 12 → 36.6 cm.
9 A bicycle wheel has diameter 0.7 m. How many complete turns to travel 100 m? (π ≈ 3.142)
Show worked solution
One turn = 3.142 × 0.7 = 2.199 m. 100 ÷ 2.199 = 45.5, so 45 complete turns.