A circle has two measurements worth knowing: the distance all the way round it (the circumference) and the space inside it (the area). Both are built from the radius: circumference = 2 × π × r, which is the same as π × d, and area = π × r × r. π is not a tidy number, so the paper always tells you which value to use — take π = 22/7 when the radius or diameter is a multiple of 7, and π = 3.14 otherwise. Read the question twice: half the marks lost here are lost by using the diameter where the formula wants the radius.
Worked example
Problem A circular badge has a diameter of 14 cm. Take π = 22/7. Find its area and its circumference.
The 14 cm is the diameter, so first halve it: 14 ÷ 2 = 7, giving a radius of 7 cm.
Area = π × r × r = 22/7 × 7 × 7. The 7s cancel, leaving 22 × 7 = 154 cm².
Circumference = π × d = 22/7 × 14 = 44 cm.
Watch out The radius is used TWICE for the area and ONCE for the circumference. Squaring it in a circumference question is the commonest slip in this topic.
Tip The paper chooses the radius to suit the π it gives you. If your answer is turning into a recurring decimal, you have almost certainly used the wrong length.