The idea in brief. "Fits exactly inside" is a measurement. The circle touching all four sides is what says the circle is as wide as the square, so the square's side is the circle's diameter, and the radius nobody printed is two steps away from a number that was. In the lesson. When a question says one shape fits exactly inside another, it is telling you a length.
Lesson video, with the working
Finding a circle's radius or diameter from a composite figure
2 min 46 s
The film teaches 1 question. The question shows first; its working is written as the film explains it.
A circle fits exactly inside a square. The perimeter of the square is 56 cm. Find the area of the circle. (Take π = 22/7.)
Area of circle = 154 cm²
Ans: 154 cm²
How to solve it
Write the area rule first: pi, times the radius, times the radius. The circle shows no radius, so find it.
The circle fits exactly inside the square, so one side of the square goes right across the circle.
Find one side from the perimeter: 56 divided by 4 is 14 centimetres.
The radius is half of that: 14 divided by 2 is 7 centimetres.
Now use the rule: 22 over 7, times 7, times 7, is 154 square centimetres.
The circle fits exactly inside, so one side of the square is what goes right across the circle. And half of that is the radius. When a question says one shape fits exactly inside another, it is telling you a length.
Practice questions with worked solutions
Questions 1 and 2 are free to try. The other 7 open in the free trial, each with its full working.
Question 1 of 9 · Basic · free to tryA round floating buoy sits in a swimming lane and touches both lane ropes…A round floating buoy sits in a…
A round floating buoy sits in a swimming lane and touches both lane ropes. The ropes are 2 m apart. Find the area of the circular front face of the buoy. (Take π = 3.14.)
Question 2 of 9 · Intermediate · free to tryFive identical circular bottle caps lie touching in a straight row, and the…Five identical circular bottle…
Five identical circular bottle caps lie touching in a straight row, and the row spans 35 cm from the left rim of the first cap to the right rim of the last. Find the area of one cap. (Take π = 3.14.)
How do you answer finding the radius or diameter questions in P6?
In these questions the radius is not printed.
What your child learns here
In these questions the radius is not printed. It has to be read from how the shapes fit together, or found by working backwards from an area or a length. They apply the Primary 6 circle outcomes in reverse, a skill composite figure questions also lean on.
Read a diameter from a fit: a circle that just fits inside a square has a diameter equal to the square's side.
Find the square's side from its perimeter or area first, when that is what is given.
Count radii along a straight line through the centres of touching circles.
Work backwards from an area: divide by pi, then find the number that times itself gives the result.
Rebuild a full circle from a quarter or half before working backwards.
Does the answer make sense?
When a circle just fits inside a square, its diameter equals the square's side, so the circle's area must be less than the square's area. A radius or diameter your child works back from an area or a fit is a length in cm or m, not square units.
How to practise these questions
The Basic questions train finding a radius that is not given but can be worked out from how the circles sit together. Intermediate questions add stacks, rows and cut corners, and working back from a leftover area. Challenge questions place a square on a circle's radii, or start from part of an area and finish at a diameter. When the length is hidden in the figure, read the written step-by-step solution.
Questions parents ask
How do you find the radius from the area of a circle? Divide the area by pi to get radius times radius, then find the number that multiplies by itself to give that result. Double it if the question wants the diameter.
What does 'fits exactly inside' mean in a circle question? It means the circle touches the shape all the way round. For a circle inside a square, the circle's diameter is the same as the side of the square, so the question is giving a length without printing it.
Is working backwards from area part of the P6 syllabus? The Primary 6 syllabus lists area and circumference of circle and composite figures. Working back from an area uses the same rule in reverse, and the worked example on this page shows each step.
