Circles and Circle Formulae

A circle is simply a round shape with a consistently curved edge.

Circle facts

 * The length across a circle which passes through the centre is called the diameter.
 * Half of the diameter is known as the radius.
 * The distance around a circle is called the circumference.
 * Any part of the circumference is called an arc.
 * A line inside a circle which does not pass through the centre is known as a chord.
 * A section of a circle bounded by two radii is called a sector.
 * A section of a circle bounded off by a chord is called a segment.
 * A line on the outside a circle which just touches the circumference is called a tangent.

Circle formulae

 * The area of a circle can be calculated by using the formula $$A = \pi r^2$$, where r is the radius of the circle.
 * The circumference of a circle can be calculated by using the formula $$C = \pi D$$, where D is the diameter of the circle.

Example questions
A circle has a radius of length 5cm.

(a) Calculate the area of the circle. Give your answer correct to 3 significant figures.


 * Step 1: Write down the formula you will need to use. In this case, it is the formula for the area of a circle.

$$A = \pi r^2$$


 * Step 2: Plug the radius into the formula:

$$A = \pi \times 5^2$$


 * Step 3: Using your calculator, work out the answer and round it to 3 significant figures.
 * It is also helpful to write '(3 s.f.)' next to your rounded answer in your working, so the examiner can see that you rounded it.

$$A = 78.5 cm^2 (3 s.f.)$$

(b) Calculate the circumference of the circle. Give your answer correct to 3 significant figures.


 * Step 1: Multiply the radius by 2 to find the circle's diameter.

$$D = 2r$$

$$D = 5 \times 2$$

$$D = 10$$


 * Step 2: Write out the formula you need to use. For this question, it is the formula used for calculating the circumference of a circle.

$$C = \pi D$$


 * Step 3: Substitute the value of the diameter into the formula:

$$C = \pi \times 10$$


 * Step 4: Work out the answer with your calculator and round appropriately:

$$C = 31.4 cm (3 s.f.)$$