GCSE Maths: Circles: vocabulary and circumference (Foundation)
Part of the GCSE Maths perimeter, area and circles chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Circles: vocabulary and circumference
Before calculating with circles we need the right words. These are examined often (Edexcel G9), so learn them.
- The circumference is the distance all the way round the circle: the perimeter of a circle.
- The centre is the point in the middle. Every point on the circle is the same distance from it.
- The radius is a straight line from the centre to the circumference.
- The diameter is a straight line from one side to the other through the centre. It is twice the radius: d = 2r.
- A chord is a straight line joining two points on the circle. (The diameter is the longest chord.)
- A tangent is a straight line that touches the circle at exactly one point.
- An arc is a part of the circumference.
- A sector is a slice of the circle between two radii and an arc, like a slice of pizza.
- A segment is the region between a chord and an arc.
The number π
Measure round any circle and divide by the distance across it. You always get a little more than 3, exactly the same number every time. That number is called π (pi) and it is 3.14159265… (the digits never end or repeat). So the circumference is a little more than 3 diameters.
Circumference C = πd or C = 2πr
The two forms are the same because d = 2r. Use πd when you know the diameter and 2πr when you know the radius.
Two ways to give the answer
With a calculator: use the π button (not 3.14), then round as the question says (decimal places or significant figures). In terms of π (an exact answer): multiply the numbers and leave the π symbol, for example C = 2 × π × 7 = 14π cm. No rounding is needed and it works without a calculator.
Perimeters involving circles
The perimeter of a semicircle is half the circumference plus the straight edge (the diameter). The perimeter of a quarter circle is a quarter of the circumference plus the two radii.
Working backwards
If you know the circumference, divide by π to get the diameter, then halve it for the radius.
Key ideas
- Radius = half the diameter. Diameter = 2 × radius.
- Circumference C = πd = 2πr. π = 3.14159…
- Use the calculator π button, and round only at the end.
- “In terms of π” means leave π as a symbol, e.g. 14π.
- Semicircle perimeter = ½πd + d. Quarter circle perimeter = ¼(2πr) + 2r.
- To find the radius from C: divide by π (that gives d), then halve.
Watch out
Do not mix up the radius and the diameter. If the circle shows 5 cm to the edge from the centre, that is the radius, and C = 2 × π × 5 = 10π, not 5π. And do not forget the straight edge on a semicircle: it is part of the perimeter.Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The diameter goes right across the circle through the centre. (The radius is half of it.)diameter = 9 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Using the radius it is 2πr.C = πd
- Substitute the number. Replace the letter with the value you know.C = π × 9
- Use the π button on your calculator. Type it in exactly as written. Do not use 3.14 unless you are told to; the button is more accurate.C = 28.2743… cm
- Round to 1 decimal place. Look at the next digit: 5 or more rounds up, 4 or less leaves it.C = 28.3 cm
Check. Estimate: π is about 3, so C is about 3 × 9 = 27 cm, close to 28.3. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The radius is the distance from the centre to the edge. The diameter goes right across the circle through the centre, so it is twice the radius.radius = 7 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Since d = 2r, this can also be written 2πr.C = 2πr
- Substitute the number. Replace the letter with the value you know.C = 2 × π × 7
- Multiply the numbers and keep the π. The question wants an exact answer in terms of π, so do not use a calculator for π. Put the number in front of π.2 × 7 = 14
C = 14π
Check. With π ≈ 3.14: 14 × 3.14 = 43.96, a sensible circumference for a circle of diameter 14 cm. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Method. The perimeter of a semicircle is the curved edge (half a circumference) plus the straight edge (the diameter). Do not forget the straight edge.
- Curved edge. Half of the circumference πd.½ × π × 10 = 15.7080… cm
- Straight edge. The diameter closes the shape.diameter = 10 cm
- Combine the pieces. Add (or subtract) the full calculator values. Do not round the pieces first, or the answer can be a little out.Perimeter = 15.7080… + 10 = 25.7080… cm
- Round to 1 decimal place. Look at the next digit: 5 or more rounds up.Perimeter = 25.7 cm
Check. Estimate with π ≈ 3: the answer should be about 25 cm, which is close to the value found. ✓
Watch out. The straight edge is part of the perimeter. Half a circle’s curve alone is not enough.
Method. Use C = πd and rearrange: divide the circumference by π to find the diameter (then halve it for the radius).
- Write the formula. Circumference = π × diameter.C = πd
- Substitute the circumference. Put the number in for C.50 = π × d
- Divide both sides by π. To undo “multiply by π” we divide by π (use the calculator button).d = 50 ÷ π = 15.91549…
- Halve it to get the radius. The radius is half the diameter.r = 15.91549… ÷ 2 = 7.95775…
- Round to 2 decimal places. Round only at the end.r = 7.96 cm
Check. Check: 2 × π × 7.96 = 50.01, close to 50. ✓
Watch out. Divide by π, do not multiply by it. Check that your answer is about a third of the circumference.
Method. Use C = πd and divide by π to find the diameter, then halve it.
- Write the formula. Circumference = π × diameter.C = πd
- Substitute the circumference. The circumference is given in terms of π, so both sides contain π.26π = π × d
- Divide both sides by π. This undoes the multiplication by π and the π’s cancel.d = 26
- Halve the diameter to get the radius. The radius is half the diameter.r = 26 ÷ 2 = 13 cm
Check. 2 × π × 13 = 26π. ✓
Watch out. Do not divide by 3.14 here: the π cancels exactly.
Exercise 18F Circles: vocabulary and circumference
Calculator allowedKey words. The centre is the middle point. The radius goes from the centre to the edge. The diameter goes across through the centre. A chord joins two points on the edge. A tangent just touches the edge. An arc is part of the edge. A sector is a slice. A segment is the part cut off by a chord.
Method. Match the description to the correct circle word.
- Read the description. Think about where the line starts and ends and whether it goes through the centre.It is the distance round the whole circle.
- Name it. Use the correct maths word.It is the circumference.
Check. Look at the labelled circle in the question to see that word on a line or curve of the right kind. ✓
Watch out. Radius is to the centre; diameter goes through the centre; a chord does not need to.
Key words. The centre is the middle point. The radius goes from the centre to the edge. The diameter goes across through the centre. A chord joins two points on the edge. A tangent just touches the edge. An arc is part of the edge. A sector is a slice. A segment is the part cut off by a chord.
Method. Match the description to the correct circle word.
- Read the description. Think about where the line starts and ends and whether it goes through the centre.It starts at the centre and ends on the circle.
- Name it. Use the correct maths word.It is the radius.
Check. Look at the labelled circle in the question to see that word on a line or curve of the right kind. ✓
Watch out. Radius is to the centre; diameter goes through the centre; a chord does not need to.
Key words. The centre is the middle point. The radius goes from the centre to the edge. The diameter goes across through the centre. A chord joins two points on the edge. A tangent just touches the edge. An arc is part of the edge. A sector is a slice. A segment is the part cut off by a chord.
Method. Match the description to the correct circle word.
- Read the description. Think about where the line starts and ends and whether it goes through the centre.It crosses the circle and goes through the centre.
- Name it. Use the correct maths word.It is the diameter.
Check. Look at the labelled circle in the question to see that word on a line or curve of the right kind. ✓
Watch out. Radius is to the centre; diameter goes through the centre; a chord does not need to.
Key words. The centre is the middle point. The radius goes from the centre to the edge. The diameter goes across through the centre. A chord joins two points on the edge. A tangent just touches the edge. An arc is part of the edge. A sector is a slice. A segment is the part cut off by a chord.
Method. Match the description to the correct circle word.
- Read the description. Think about where the line starts and ends and whether it goes through the centre.Both ends are on the circle.
- Name it. Use the correct maths word.It is the chord.
Check. Look at the labelled circle in the question to see that word on a line or curve of the right kind. ✓
Watch out. Radius is to the centre; diameter goes through the centre; a chord does not need to.
Key words. The centre is the middle point. The radius goes from the centre to the edge. The diameter goes across through the centre. A chord joins two points on the edge. A tangent just touches the edge. An arc is part of the edge. A sector is a slice. A segment is the part cut off by a chord.
Method. Match the description to the correct circle word.
- Read the description. Think about where the line starts and ends and whether it goes through the centre.It touches the circle but does not cross into it.
- Name it. Use the correct maths word.It is the tangent.
Check. Look at the labelled circle in the question to see that word on a line or curve of the right kind. ✓
Watch out. Radius is to the centre; diameter goes through the centre; a chord does not need to.
Key words. The centre is the middle point. The radius goes from the centre to the edge. The diameter goes across through the centre. A chord joins two points on the edge. A tangent just touches the edge. An arc is part of the edge. A sector is a slice. A segment is the part cut off by a chord.
Method. Match the description to the correct circle word.
- Read the description. Think about where the line starts and ends and whether it goes through the centre.It is a piece of the curved edge.
- Name it. Use the correct maths word.It is the arc.
Check. Look at the labelled circle in the question to see that word on a line or curve of the right kind. ✓
Watch out. Radius is to the centre; diameter goes through the centre; a chord does not need to.
Method. Look at the straight edges of each shaded shape.
- Left picture. It has two straight edges that are both radii meeting at the centre, and one curved edge (an arc).Two radii + an arc = a sector.
- Right picture. It has one straight edge (a chord, which does not reach the centre) and one curved edge.A chord + an arc = a segment.
Check. A sector looks like a slice of pizza; a segment looks like the cap left when a chord cuts the circle. ✓
Watch out. A segment is cut off by a chord. A sector is cut off by two radii.
Method. The diameter is twice the radius.
- Write the rule. The diameter goes across through the centre, which is two radii.d = 2 × r
- Substitute. The radius is 6 cm.2 × 6 = 12 cm
Check. 12 ÷ 2 = 6, the radius. ✓
Method. The radius is half the diameter.
- Write the rule. The radius goes only to the centre, which is half way across.r = d ÷ 2
- Substitute. The diameter is 15 cm.15 ÷ 2 = 7.5 cm
Check. 2 × 7.5 = 15. ✓
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The diameter goes right across the circle through the centre. (The radius is half of it.)diameter = 9 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Using the radius it is 2πr.C = πd
- Substitute the number. Replace the letter with the value you know.C = π × 9
- Use the π button on your calculator. Type it in exactly as written. Do not use 3.14 unless you are told to; the button is more accurate.C = 28.2743… cm
- Round to 1 decimal place. Look at the next digit: 5 or more rounds up, 4 or less leaves it.C = 28.3 cm
Check. Estimate: π is about 3, so C is about 3 × 9 = 27 cm, close to 28.3. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The radius is the distance from the centre to the edge. The diameter goes right across the circle through the centre, so it is twice the radius.radius = 7 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Since d = 2r, this can also be written 2πr.C = 2πr
- Substitute the number. Replace the letter with the value you know.C = 2 × π × 7
- Use the π button on your calculator. Type it in exactly as written. Do not use 3.14 unless you are told to; the button is more accurate.C = 43.9823… cm
- Round to 1 decimal place. Look at the next digit: 5 or more rounds up, 4 or less leaves it.C = 44.0 cm
Check. Estimate: π is about 3, so C is about 3 × 14 = 42 cm, close to 44.0. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The radius is the distance from the centre to the edge. The diameter goes right across the circle through the centre, so it is twice the radius.radius = 5 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Since d = 2r, this can also be written 2πr.C = 2πr
- Substitute the number. Replace the letter with the value you know.C = 2 × π × 5
- Multiply the numbers and keep the π. The question wants an exact answer in terms of π, so do not use a calculator for π. Put the number in front of π.2 × 5 = 10
C = 10π
Check. With π ≈ 3.14: 10 × 3.14 = 31.40, a sensible circumference for a circle of diameter 10 cm. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The radius is the distance from the centre to the edge. The diameter goes right across the circle through the centre, so it is twice the radius.radius = 5 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Since d = 2r, this can also be written 2πr.C = 2πr
- Substitute the number. Replace the letter with the value you know.C = 2 × π × 5
- Use the π button on your calculator. Type it in exactly as written. Do not use 3.14 unless you are told to; the button is more accurate.C = 31.4159… cm
- Round to 1 decimal place. Look at the next digit: 5 or more rounds up, 4 or less leaves it.C = 31.4 cm
Check. Estimate: π is about 3, so C is about 3 × 10 = 30 cm, close to 31.4. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The diameter goes right across the circle through the centre. (The radius is half of it.)diameter = 12 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Using the radius it is 2πr.C = πd
- Substitute the number. Replace the letter with the value you know.C = π × 12
- Multiply the numbers and keep the π. The question wants an exact answer in terms of π, so do not use a calculator for π. Put the number in front of π.C = 12π
Check. With π ≈ 3.14: 12 × 3.14 = 37.68, a sensible circumference for a circle of diameter 12 cm. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The radius is the distance from the centre to the edge. The diameter goes right across the circle through the centre, so it is twice the radius.radius = 12.5 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Since d = 2r, this can also be written 2πr.C = 2πr
- Substitute the number. Replace the letter with the value you know.C = 2 × π × 12.5
- Use the π button on your calculator. Type it in exactly as written. Do not use 3.14 unless you are told to; the button is more accurate.C = 78.5398… cm
- Round to 3 significant figures. Look at the next digit: 5 or more rounds up, 4 or less leaves it.C = 78.5 cm
Check. Estimate: π is about 3, so C is about 3 × 25 = 75 cm, close to 78.5. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Method. Replace π by 3, a number that is easy to use.
- Use the formula. C = πd.C ≈ 3 × 10
- Multiply. 3 × 10 = 30 cm
Check. π is a bit bigger than 3, so the real answer is a bit more than 30. ✓
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The diameter goes right across the circle through the centre. (The radius is half of it.)diameter = 10 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Using the radius it is 2πr.C = πd
- Substitute the number. Replace the letter with the value you know.C = π × 10
- Use the π button on your calculator. Type it in exactly as written. Do not use 3.14 unless you are told to; the button is more accurate.C = 31.4159… cm
- Round to 1 decimal place. Look at the next digit: 5 or more rounds up, 4 or less leaves it.C = 31.4 cm
Check. Estimate: π is about 3, so C is about 3 × 10 = 30 cm, close to 31.4. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Method. The perimeter of a semicircle is the curved edge (half a circumference) plus the straight edge (the diameter). Do not forget the straight edge.
- Curved edge. Half of the circumference πd.½ × π × 10 = 15.7080… cm
- Straight edge. The diameter closes the shape.diameter = 10 cm
- Combine the pieces. Add (or subtract) the full calculator values. Do not round the pieces first, or the answer can be a little out.Perimeter = 15.7080… + 10 = 25.7080… cm
- Round to 1 decimal place. Look at the next digit: 5 or more rounds up.Perimeter = 25.7 cm
Check. Estimate with π ≈ 3: the answer should be about 25 cm, which is close to the value found. ✓
Watch out. The straight edge is part of the perimeter. Half a circle’s curve alone is not enough.
Method. The perimeter of a quarter circle is the curved edge (a quarter of the circumference) plus the two straight edges (two radii).
- Curved edge. A quarter of the circumference 2πr.¼ × 2 × π × 8 = ¼ × 16π = 4π cm
- Two straight edges. Both are radii.2 × 8 = 16 cm
- Combine the pieces. Add. Whole numbers go with whole numbers and the π terms go with π terms. A number and a π term cannot be merged into one, so leave them as a sum.Perimeter = 4π + 16 = (16 + 4π) cm
Check. Estimate with π ≈ 3: the answer should be about 28 cm, which is close to the value found. ✓
Watch out. Add the two radii. The perimeter has three edges: one curved and two straight.
Method. The perimeter of a quarter circle is the curved edge (a quarter of the circumference) plus the two straight edges (two radii).
- Curved edge. A quarter of the circumference 2πr.¼ × 2 × π × 8 = ¼ × 16π = 12.5664… cm
- Two straight edges. Both are radii.2 × 8 = 16 cm
- Combine the pieces. Add (or subtract) the full calculator values. Do not round the pieces first, or the answer can be a little out.Perimeter = 12.5664… + 16 = 28.5664… cm
- Round to 1 decimal place. Look at the next digit: 5 or more rounds up.Perimeter = 28.6 cm
Check. Estimate with π ≈ 3: the answer should be about 28 cm, which is close to the value found. ✓
Watch out. Add the two radii. The perimeter has three edges: one curved and two straight.
Method. Use C = πd and divide by π to find the diameter, then halve it.
- Write the formula. Circumference = π × diameter.C = πd
- Substitute the circumference. The circumference is given in terms of π, so both sides contain π.26π = π × d
- Divide both sides by π. This undoes the multiplication by π and the π’s cancel.d = 26
- Halve the diameter to get the radius. The radius is half the diameter.r = 26 ÷ 2 = 13 cm
Check. 2 × π × 13 = 26π. ✓
Watch out. Do not divide by 3.14 here: the π cancels exactly.
Method. Use C = πd and rearrange: divide the circumference by π to find the diameter (then halve it for the radius).
- Write the formula. Circumference = π × diameter.C = πd
- Substitute the circumference. Put the number in for C.50 = π × d
- Divide both sides by π. To undo “multiply by π” we divide by π (use the calculator button).d = 50 ÷ π = 15.91549…
- Halve it to get the radius. The radius is half the diameter.r = 15.91549… ÷ 2 = 7.95775…
- Round to 2 decimal places. Round only at the end.r = 7.96 cm
Check. Check: 2 × π × 7.96 = 50.01, close to 50. ✓
Watch out. Divide by π, do not multiply by it. Check that your answer is about a third of the circumference.
Key words. The circumference is the distance round a circle. The diameter is the distance across through the centre; the radius is half of that. π (pi) is the number 3.14159… you get by dividing any circumference by its diameter.
Method. The circumference of a circle is π × diameter, or 2 × π × radius. Find the diameter or radius, substitute, and calculate.
- Write down what is given. The diameter goes right across the circle through the centre. (The radius is half of it.)diameter = 70 cm
- Choose the formula. The circumference is the distance round the circle. It is always about 3.14 times the diameter, and that number is π. Using the radius it is 2πr.C = πd
- Substitute the number. Replace the letter with the value you know.C = π × 70
- Use the π button on your calculator. Type it in exactly as written. Do not use 3.14 unless you are told to; the button is more accurate.C = 219.9115… cm
- Round to 3 significant figures. Look at the next digit: 5 or more rounds up, 4 or less leaves it.C = 220 cm
Check. Estimate: π is about 3, so C is about 3 × 70 = 210 cm, close to 220. ✓
Watch out. If you are given the diameter use πd. If you are given the radius, double it (2πr). Do not mix them up.
Method. Change 1 km to the same unit as the wheel, divide by the circumference (using the unrounded value), and round up.
- Change 1 km to centimetres. 1 km = 1000 m = 100 000 cm.1 km = 100 000 cm
- Divide by the circumference. Each turn covers C = π × 70 cm. Use the calculator value without rounding.100 000 ÷ (π × 70) = 100 000 ÷ 219.911… = 454.73…
- Round up. 454 complete turns would fall short of 1 km, so we need the next whole number.455 turns
Check. 455 × 219.911… = 100,059.7… cm, which is at least 100 000 cm; 454 turns is only 99,839.8… cm. ✓
Watch out. Round up, not to the nearest: a part-turn does not finish the distance.
Method. The fence goes round the pond, so use the circumference. Then multiply by the cost per metre.
- Circumference. The diameter is 3.5 m, so use C = πd.C = π × 3.5 = 10.9956… m
- Cost. Multiply the circumference by £9 per metre. Do not round before you multiply.10.9956… × 9 = £98.9602…
- Round to the nearest penny. That is 2 decimal places.£98.96
Check. Estimate: 3.5 × 3 = 10.5 m and 10.5 × 9 = £94.50, close to £98.96. ✓
Watch out. Fencing goes round the edge, so use the circumference, not the area.
Method. Check which formula Sam used.
- Spot the mistake. Sam multiplied π by the radius. But C = πd, and the diameter is twice the radius.Sam used π × 5, but d = 2 × 5 = 10.
- Correct it. C = πd = 2πr.C = π × 10 = 10π cm
Check. 2 × π × 5 = 10π. ✓
Watch out. Use the diameter with πd, or 2πr with the radius.
Method. Work out the circumference of the circle and the perimeter of the square, then compare.
- Circumference of the circle. C = πd.π × 10 = 31.4 cm (1 d.p.)
- Perimeter of the square. Four equal sides.4 × 8 = 32 cm
- Compare. 32 is bigger than 31.4.The square has the bigger perimeter, but only just.
Check. π × 10 is a little more than 3 × 10 = 30, so about 31 — less than 32. ✓
Watch out. Do not round π to 3 here: it would make the circle look much smaller.
Method. Divide the circumference by the diameter and compare with π.
- Write the two measurements. The string measures the circumference.circumference = 22 cm, diameter = 7 cm
- Divide. Circumference ÷ diameter.22 ÷ 7 = 3.1429…
- Say what it shows. Compare with π = 3.14159…The answer is very close to π. It shows that the circumference of a circle is about π times its diameter.
Check. π × 7 = 21.99… ≈ 22. ✓
Watch out. 22 ÷ 7 is only an approximation of π, not its exact value.