Circles in shapes: step-by-step example
29 October 2026
Understanding how circles fit inside other shapes is a common part of 11+ maths. Children often see questions where a circle is drawn inside a square or rectangle, and they need to work out the radius or diameter. This type of problem helps build spatial awareness and links shape knowledge to real calculations. If your child is practising for the 11+ and you've searched for maths.com uk style questions, this example is just what you need.
Worked example
A circle is drawn inside a square so that it touches all four sides. The square has a side length of 8 cm. Find the radius of the circle.
Step 1: The circle touches all sides, so its diameter is the same as the side length of the square.
Step 2: The side length of the square is 8 cm, so the diameter of the circle is 8 cm.
Step 3: The radius is half the diameter. 8 cm ÷ 2 = 4 cm.
The correct answer is 4 cm.
After working through this example, your child will spot when a circle fits perfectly inside a square and know how to find its radius. They'll be ready to tackle similar questions on circles in shapes, with more practice available in the next set of problems.
