Area and circumference of a circle
The circumference is π times the diameter, O = π · d. The area is π times the radius squared, A = π · r². π is about 3.14. A radius of 5 cm gives a circumference of about 31.4 cm and an area of about 78.5 cm².
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Radius, diameter and π
The radius r goes from the centre to the edge. The diameter d goes straight through the centre, from edge to edge.
d = 2 · r r = d ÷ 2
Three diameters and a little more fit around any circle. That number is π ≈ 3.14. Because 3.14 is rounded, we write ≈ in the answer. The π button gives a slightly more exact answer.
The formulas
| What we want | Formula | Unit |
|---|---|---|
| Circumference | O = π · d or O = 2 · π · r | cm, m |
| Area | A = π · r² | cm², m² |
r² means r · r, not r · 2. With r = 5, we get r² = 25.
Is the answer reasonable?
- The circumference is a little more than 3 · d.
- The area is a little more than 3 · r².
- We do not round until the last step.
Example
Example 1: the circumference of a circle with diameter 10 cm
We want to know how far it is around the circle. The diameter is known, so we use O = π · d.
We put the diameter into the formula.
O = π · 10
We use π ≈ 3.14.
O ≈ 3.14 · 10 = 31.4
The circumference is a length, so the unit is cm.
O ≈ 31.4 cm
A little more than three diameters, 3 · 10 = 30 cm. 31.4 cm is reasonable.
Example 2: how big is a pizza with diameter 30 cm?
We want to find the area. The area formula uses the radius, so we find that first.
The radius is half the diameter.
r = 30 ÷ 2 = 15
We work out r², which is the radius times itself.
r² = 15 · 15 = 225
We multiply by π ≈ 3.14.
A ≈ 3.14 · 225 = 706.5
The pizza is about 706.5 cm². With the π button we get 706.86 cm².
A ≈ 706.5 cm²
A little more than 3 · 225 = 675 cm². 706.5 cm² is reasonable.
Pitfalls
Putting the diameter into the area formula: π · 30² for a pizza with diameter 30 cm.
The area formula uses the radius. Divide the diameter by two first, otherwise the area is four times too large.
Thinking that r² means r · 2, so that r = 5 gives r² = 10.
5² = 5 · 5 = 25, like the area of a square with side 5.
Answering in cm² for a circumference or in cm for an area.
Circumference is a distance: cm. Area is a surface: cm².
Practise on your own
0 of 4 correct1A circle has radius 3 cm. What is the circumference? Use π ≈ 3.14.
2A circle has radius 6 cm. What is the area? Use π ≈ 3.14.
3A round rug has diameter 14 dm. What is the area? Use π ≈ 3.14.
4A bicycle wheel has circumference 157 cm. What is the diameter? Use π ≈ 3.14.
Common questions
Should I use 3.14 or the π button?
Follow the task. If it does not say, both work, but the π button is more exact. Write ≈ and say which value you used.
How do you work out the radius if you know the area?
Divide the area by π and take the square root. An area of 50.24 cm² gives r² = 50.24 ÷ 3.14 = 16, so r = √16 = 4 cm.
How do you find the area of a semicircle?
Work out the area of the whole circle and divide by two. The perimeter of the semicircle is half the circle's circumference plus the diameter.
Read also
- Years 4–9Area and perimeterHow do you work out area and perimeter?
- Years 5–9Volume of a cuboid, prism and cylinderHow do you work out volume?
- Years 7–9 and upper secondaryPowers and the laws of exponentsHow do you calculate with powers?
- Years 4–9Order of operations (BIDMAS)What is the order of operations?
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