Year 6: Parts of a circle and the circumference
Part of the Year 6 angles, shapes and circles chapter. Chapter overview · whole chapter on one page
Parts of a circle and the circumference
A circle has a centre. The radius goes from the centre to the edge. The diameter goes from one side of the circle to the other, through the centre. The diameter is twice the radius, so the radius is half the diameter.
The circumference is the distance all the way round the edge. For every circle, the circumference is about 3 times the diameter. The exact number is called pi (π). In this book we use two values, and the question always tells you which to use:
- π = 3.14
- π = 22/7 (good when the diameter is a multiple of 7)
The formula is C = π × d, where d is the diameter.
Key ideas
- The radius goes from the centre to the edge.
- The diameter goes across the circle through the centre.
- Diameter = 2 × radius, and radius = diameter ÷ 2.
- Circumference = π × diameter.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Double the radius to find the diameter.
- Remember: the diameter is twice the radius. The diameter goes across the whole circle, through the centre, so it is two radii.diameter = 2 × radius
- Multiply the radius by 2. This gives the diameter.2 × 5 = 10
- Write the answer. The diameter is in the same unit as the radius.10
Check. 10 ÷ 2 = 5, the radius. ✓
Watch out. The diameter is double the radius, not half of it.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Multiply the diameter by 3.14.
- Write the formula. The circumference is pi times the diameter.C = π × d
- Put in the numbers. The question says to use π = 3.14.C = 3.14 × 12
- Work out the product. Multiply the diameter by pi.12 × 3.14 = 37.68
- Write the answer. The circumference is in the same unit as the diameter.37.68
Check. 37.68 ÷ 3.14 = 12. ✓
Watch out. The circumference is about three times the diameter, but use the exact value of pi given in the question.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Divide the diameter by 7, then multiply by 22.
- Write the formula. The circumference is pi times the diameter.C = π × d
- Put in the numbers. The question says to use π = 22/7.C = 22/7 × 14
- Work out the product. Multiply the diameter by pi.14 ÷ 7 = 2, then 2 × 22 = 44
- Write the answer. The circumference is in the same unit as the diameter.44
Check. 44 ÷ 22 × 7 = 14. ✓
Watch out. The circumference is about three times the diameter, but use the exact value of pi given in the question.
Exercise 10D Practice: radius, diameter and circumference
Non-calculatorKey words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Think about where the line starts and ends.
- Find the line. It starts at the centre and ends on the edge.centre to edge
- Name it. A line from the centre to the edge is called the radius.radius
Check. The diameter is twice this line, and goes through the centre. ✓
Watch out. The radius is half of the diameter. It starts at the centre.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Double the radius to find the diameter.
- Remember: the diameter is twice the radius. The diameter goes across the whole circle, through the centre, so it is two radii.diameter = 2 × radius
- Multiply the radius by 2. This gives the diameter.2 × 6 = 12
- Write the answer. The diameter is in the same unit as the radius.12
Check. 12 ÷ 2 = 6, the radius. ✓
Watch out. The diameter is double the radius, not half of it.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Halve the diameter to find the radius.
- Remember: the radius is half the diameter. The radius goes from the centre to the edge, which is half of the way across.radius = diameter ÷ 2
- Divide the diameter by 2. This gives the radius.14 ÷ 2 = 7
- Write the answer. The radius is in the same unit as the diameter.7
Check. 7 + 7 = 14, the diameter. ✓
Watch out. Halve the diameter to get the radius. Do not double it.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Multiply the diameter by 3.14.
- Write the formula. The circumference is pi times the diameter.C = π × d
- Put in the numbers. The question says to use π = 3.14.C = 3.14 × 10
- Work out the product. Multiply the diameter by pi.10 × 3.14 = 31.4
- Write the answer. The circumference is in the same unit as the diameter.31.4
Check. 31.4 ÷ 3.14 = 10. ✓
Watch out. The circumference is about three times the diameter, but use the exact value of pi given in the question.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Divide the diameter by 7, then multiply by 22.
- Write the formula. The circumference is pi times the diameter.C = π × d
- Put in the numbers. The question says to use π = 22/7.C = 22/7 × 7
- Work out the product. Multiply the diameter by pi.7 ÷ 7 = 1, then 1 × 22 = 22
- Write the answer. The circumference is in the same unit as the diameter.22
Check. 22 ÷ 22 × 7 = 7. ✓
Watch out. The circumference is about three times the diameter, but use the exact value of pi given in the question.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Double the radius to get the diameter, then multiply the diameter by 3.14.
- Find the diameter first. The diameter is twice the radius.2 × 3 = 6
- Write the formula. The circumference is pi times the diameter.C = π × d
- Put in the numbers. The question says to use π = 3.14.C = 3.14 × 6
- Work out the product. Multiply the diameter by pi.6 × 3.14 = 18.84
- Write the answer. The circumference is in the same unit as the radius.18.84
Check. 18.84 ÷ 3.14 = 6, the diameter. ✓
Watch out. Use the diameter in the formula, not the radius.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Divide the circumference by 3.14 to find the diameter.
- Write the formula. The circumference is pi times the diameter.C = 3.14 × d
- Undo the multiplication by 3.14. Divide the circumference by 3.14 to find the diameter.31.4 ÷ 3.14 = 10
- Write the answer. The diameter is in the same unit as the circumference.10
Check. 10 × 3.14 = 31.4. ✓
Watch out. Divide the circumference by pi. Do not divide it by 2.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Multiply the diameter by 3.14.
- Write the formula. The circumference is pi times the diameter.C = π × d
- Put in the numbers. The question says to use π = 3.14.C = 3.14 × 2.5
- Work out the product. Multiply the diameter by pi.2.5 × 3.14 = 7.85
- Write the answer. The circumference is in the same unit as the diameter.7.85
Check. 7.85 ÷ 3.14 = 2.5. ✓
Watch out. The circumference is about three times the diameter, but use the exact value of pi given in the question.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Multiply the diameter by 3.14.
- Write the formula. The circumference is pi times the diameter.C = π × d
- Put in the numbers. The question says to use π = 3.14.C = 3.14 × 70
- Work out the product. Multiply the diameter by pi.70 × 3.14 = 219.8
- Write the answer. The circumference is in the same unit as the diameter.219.8
Check. 219.8 ÷ 3.14 = 70. ✓
Watch out. The circumference is about three times the diameter, but use the exact value of pi given in the question.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Double the radius to get the diameter, then multiply the diameter by 3.14.
- Find the diameter first. The diameter is twice the radius.2 × 4 = 8
- Write the formula. The circumference is pi times the diameter.C = π × d
- Put in the numbers. The question says to use π = 3.14.C = 3.14 × 8
- Work out the product. Multiply the diameter by pi.8 × 3.14 = 25.12
- Write the answer. The circumference is in the same unit as the radius.25.12
Check. 25.12 ÷ 3.14 = 8, the diameter. ✓
Watch out. Use the diameter in the formula, not the radius.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Compare the claim with the value of pi.
- Write the formula. Circumference = π × diameter.C = π × d
- Compare pi with 3. Pi is 3.14, which is a little more than 3.3.14 is not 3
- Write the answer. Ruby is not exactly right, because the circumference is about 3.14 times the diameter.No
Check. For a diameter of 10 cm, 3 times 10 is 30 cm, but the circumference is 31.4 cm. ✓
Watch out. Three is only an estimate. The exact multiplier is pi, which is 3.14 to two decimal places.
Key words. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is two radii. The circumference is the distance all the way round the edge.
Method. Find the diameter from the circumference using 22/7, then halve it.
- Write the formula. The circumference is 22/7 times the diameter.C = 22/7 × d
- Find the diameter. Divide the circumference by 22, then multiply by 7.22 ÷ 22 × 7 = 7
- Halve the diameter to get the radius. The diameter is twice the radius.7 ÷ 2 = 3.5
- Write the answer. The radius is in the same unit as the circumference.3.5
Check. 3.5 + 3.5 = 7, and 22/7 × 7 = 22. ✓
Watch out. Halve the diameter to get the radius at the end.
Watch out
Common mistake: using the radius in the formula C = π × d. Double the radius first to get the diameter, then multiply by pi. Also, the diameter is double the radius, not half of it.
Exam tip
Write the number of pi that the question gives, such as 3.14, in your working. This shows the examiner which value you used.