These questions ask you to identify circle parts, move between radius and diameter, or calculate the distance around a circle and the surface inside it. The wording tells you whether π stays in the result or is replaced by 3.14.
Match the part, measure and formula
| What you need | Rule and a quick example |
|---|---|
| Radius and diameter | Double a radius to get the diameter; halve a diameter to get the radius. A radius of 8 gives a diameter of 16. |
| Circumference from diameter | Multiply the diameter by π. A diameter of 9 gives a circumference of 9π. |
| Circumference from radius | Double the radius first, then multiply by π. A radius of 2.5 gives a circumference of 5π. |
| Area from radius | Multiply the radius by itself, then by π. A radius of 4 gives an area of 16π units of area. |
Keep π symbolic when the question asks for a result in terms of π. When a value such as 3.14 is stated, substitute it only after choosing the right formula. Units provide a final check: circumference is a length, while area is measured in units such as cm².
Where circle work goes wrong
| Tempting route | How to reject it |
|---|---|
| Call any straight circle segment a diameter | A diameter must join two points on the circle and pass through the centre. A centre-to-edge segment is only half as long. |
| Confuse a chord with the curved boundary | A chord is straight. The circumference follows the curve all the way around. |
| Double when changing a diameter to a radius | The radius is the smaller measure. Divide the full width into two equal halves. |
| Put the radius straight into the diameter form of the circumference rule | That loses the other half of the width. Double the radius before multiplying by π. |
| Use the circumference rule for area | The distance around uses the full width once; the surface inside uses the radius twice by multiplying it by itself. |
| Multiply a stated diameter by itself in the area rule | Area requires the radius. Halve a stated full width before multiplying it by itself. |
Try it
A circle has a radius of 5 centimetres. Enter the number of centimetres in its diameter.
A circle has a diameter of 10 centimetres. What is its circumference? Give the answer in terms of π.
- 5π centimetres
- 10π centimetres
- 20π centimetres
- 100π centimetres
A circle has a radius of 10 centimetres, and π is to be taken as exactly 3.14. Select all the statements that are true about the area of this circle.
- Its area is 314 square centimetres.
- Its area is 62.8 square centimetres.
- Its area is 314 centimetres.
- Its area has to be reported in square units rather than plain centimetres, because two lengths were multiplied.