Formula sheet
Area of circle
πr² is given on the exam formula sheet. You must still remember it uses the radius (not the diameter), that r is squared, and that the answer is an area in square units.
What the symbols mean
- r Radius, distance from the centre to the edge (length unit). Halve the diameter if only d is given.
- π Pi ≈ 3.142 or 22/7; ratio of circumference to diameter.
Given in the exam, or memorise?
πr² is given on the exam formula sheet. You must still remember it uses the radius (not the diameter), that r is squared, and that the answer is an area in square units.
Why it works
A circle can be reshaped into a near-rectangle.
- Cut the circle into many thin sectors and lay them alternately.
- They form a shape close to a rectangle of height r and length πr (half the circumference).
- Its area r × πr = πr².
Worked example 1
Find the area of a circle of radius 14 cm. (Use π = 22/7)
- Area = πr²
- = 22/7 × 14²
- = 22/7 × 196
- = 22 × 28 = 616
Worked example 2
A circle has area 154 cm². Find its radius.
(Use π = 22/7)
- Area = πr²
- 154 = 22/7 × r²
- r² = 154 × 7 ÷ 22 = 49
- r = √49 = 7
Where students go wrong
- Putting the diameter into r, always halve the diameter first.
- Forgetting to square r, so you compute πr instead of πr².
- Squaring wrongly, e.g. writing 14² as 28 instead of 196.
- Giving the answer in cm instead of cm².
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
The question gives me the diameter. What do I do?
Halve it to get the radius first, because πr² uses r, not d. For example a diameter of 20 cm gives r = 10 cm, so the area is π × 10² = 100π.
Dropping the diameter straight into the formula would make the area four times too big.
Why is the area formula squared but circumference is not?
Area measures a two-dimensional region, so it grows with the square of the radius, that is why r is squared and the unit is cm². Circumference measures a one-dimensional length around the circle, so it grows in step with r and stays in cm.
The squared unit is a useful reminder of which formula you are using.
Is πr² given in SPM or must I memorise it?
It is printed on the SPM formula sheet, so you do not memorise it. What you are graded on is applying it correctly: use the radius, square it, multiply by π, and write cm².
Knowing the formula is available lets you focus on clean substitution and correct units instead of recall.