This worksheet applies circle formulas, teaching students to calculate the circumference and area of a circle, and to work backwards from a given circumference or area to find its radius. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Circumference: C = 2πr = πd. Area: A = πr².
- A quick rough estimate for a circle's area is 3r² (since π ≈ 3.14 is close to 3) — always an underestimate.
- To work backwards from area to radius: r² = A ÷ π, then take the square root.
- To work backwards from circumference to radius: r = C ÷ (2π).
- An annulus (a ring shape) is the area between two circles with the same centre: outer circle's area minus inner circle's area.
What your child will practise:
- Applying C = 2πr or C = πd to find a circle's circumference from its radius or diameter.
- Applying A = πr² to find a circle's area.
- Rearranging the area or circumference formula to find the radius from a known area or circumference.
- Finding the area of a semicircle (half the full circle's area) or its perimeter (half circumference plus the diameter).
- Finding the area of a ring shape (annulus) by subtracting the inner circle's area from the outer circle's area.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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