Circles

A circle has no straight sides and no corners, so the rectangle formulas are useless here. Instead, circles bring in one special number — pi — that links the distance across a circle to the distance around it. This is a P6 topic, and once you know which formula uses the diameter and which uses the radius, even tricky shaded figures become a few clean steps.

Parents: ask your child to predict whether a question needs the radius or the diameter before they reveal. The "Method tip" boxes name the exact formula a PSLE marker rewards. In this note we take pi as 3.14.

By the end you'll be able to find the radius and diameter, the circumference, the area, and work with semicircles, quarter circles and shaded figures. Let's go round.

Radius and diameter

The radius is the distance from the centre to the edge. The diameter goes all the way across through the centre. The key link is simple: the diameter is twice the radius.

So if the radius is 5 cm, the diameter is 2 × 5 = 10 cm. And if the diameter is 14 cm, the radius is 14 ÷ 2 = 7 cm. Always check which one a question gives you, because the two formulas ahead need different ones.

Circumference: pi times diameter

The circumference is the perimeter of a circle. The formula is pi × diameter. Since the diameter is twice the radius, you can also write it as pi × 2 × radius — but pi × diameter is the cleanest.

For example, a circle with diameter 10 cm has circumference 3.14 × 10 = 31.4 cm. If you are only given the radius, double it to get the diameter first. Circumference is a distance, so the unit is plain cm.

Area: pi times radius times radius

The area of a circle is pi × radius × radius. This one uses the radius, not the diameter — that is the difference students most often miss. If you are given the diameter, halve it to the radius first.

For example, a circle with radius 10 cm has area 3.14 × 10 × 10 = 3.14 × 100 = 314 square cm. Because you multiply two lengths, the area unit is square cm.

Semicircles, quarter circles and shaded figures

A semicircle is half a circle, and a quarter circle is one fourth. To find their area, work out the full circle's area first, then take half or a quarter.

For example, a semicircle with radius 10 cm has area (3.14 × 10 × 10) ÷ 2 = 314 ÷ 2 = 157 square cm. For a shaded figure, find the bigger area and subtract the part that is not shaded.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. A circle has a radius of 6 cm. What is its diameter?

   3 cm12 cm36 cm

2. Taking pi as 3.14, what is the circumference of a circle with diameter 10 cm?

   31.4 cm78.5 cm15.7 cm

3. Taking pi as 3.14, what is the area of a circle with radius 10 cm?

   31.4 square cm62.8 square cm314 square cm

4. A circle has a diameter of 8 cm. Which length do you use to find its AREA?

   The radius, 4 cmThe diameter, 8 cmThe circumference

5. Taking pi as 3.14, what is the area of a semicircle with radius 10 cm?

   314 square cm157 square cm78.5 square cm

6. Taking pi as 3.14, what is the circumference of a circle with radius 5 cm?

   31.4 cm15.7 cm78.5 cm

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