The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Circles – worksheets to print
Terms of the circle (radius, diameter, chord, secant, tangent), working out circumference and area, working back to the radius, semicircles, quarter circles, rings and composite figures.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Circles: explained simply
All points on a circle are the same distance from the centre. You work out how long the circle is (circumference) and how big its area is.
How to work it out
- The diameter is twice as long as the radius: d = 2 · r. A chord joins two points of the circle, a secant is the straight line through those points, and a tangent touches the circle at just one point.
- Circumference C = 2 · π · r = π · d, area A = π · r · r. The sheet says whether you use π ≈ 3.14 or the π key of the calculator.
An example, step by step
A circle has radius 5 cm. Work out the circumference and the area with π ≈ 3.14.
- C = 2 · 3.14 · 5 cm = 31.4 cm.
- A = 3.14 · 5 cm · 5 cm = 78.5 cm².
- The circumference is a length in cm, the area has the unit cm².
Understand other variations
Parts of circles and rings
A semicircle has half the area of the circle, and its perimeter includes the diameter. For a quarter circle divide the area by 4; its perimeter includes two radii. For a ring, A = π · (R² − r²): the outer area minus the inner area.
Working backwards
If C = 31.4 cm is given, r = C : (2 · π) = 31.4 : 6.28 = 5 cm. For an area, work out r² = A : π and then take the square root.
Your turn
A circle has diameter 10 cm. Work out the circumference (π ≈ 3.14).
Show the answer and method
C = 3.14 · 10 cm = 31.4 cm.
Ready-made worksheets: Circles
Click the picture to see the worksheet large and print it. “Use” opens it in the editor.