Shape and space · Ages 10–11

Parts of a circle worksheet

Covers: Radius and diameter

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Shape and space · Ages 10–11

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A circle's diameter is 6 cm. How many centimetres is its radius?
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2.A circle's radius is 13 cm. How many centimetres is its diameter?
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3.A circle's diameter is 28 cm. How many centimetres is its radius?
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4.A circle's radius is 34 cm. How many centimetres is its diameter?
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5.A line is drawn inside a circle of radius 26 cm with both ends on the circle. What is the longest it can be, in cm?
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6.A line is drawn inside a circle of radius 9 cm with both ends on the circle. What is the longest it can be, in cm?
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13.7 round coasters of radius 15 cm are laid touching in a straight line. How many centimetres long is the line?
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14.Ka-yee draws the biggest circle that fits on a square of paper 8 cm wide. How far apart, in cm, should the compass legs be?
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15.A round pond is 36 m across. May walks straight from its edge to its centre. What is the least distance, in metres?
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16.A box's base is 50 cm by 16 cm. At most how many round biscuits 10 cm across fit flat in it, laid in rows, not stacked?
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17.7 round coasters of radius 13 cm are laid touching in a straight line. How many centimetres long is the line?
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18.A box's base is 47 cm by 31 cm. At most how many round biscuits 5 cm across fit flat in it, laid in rows, not stacked?
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Show the answers and working

Parts of a circle worksheet: Answers and working

1. 3 cm
A radius is half a diameter. Split the 6 cm diameter into two equal parts.
Radius = diameter ÷ 2 = 6 ÷ 2 = 3.
2. 26 cm
A diameter is two radii end to end. The radius is 13 cm: how does the diameter compare?
Diameter = 2 × radius = 2 × 13 = 26.
3. 14 cm
A radius is half a diameter. Split the 28 cm diameter into two equal parts.
Radius = diameter ÷ 2 = 28 ÷ 2 = 14.
4. 68 cm
A diameter is two radii end to end. The radius is 34 cm: how does the diameter compare?
Diameter = 2 × radius = 2 × 34 = 68.
5. 52 cm
Of the lines with both ends on the circle, which is longest? Think about whether it passes through the centre.
Of all lines with both ends on the circle, the diameter through the centre is longest: 2 × 26 = 52.
6. 18 cm
Of the lines with both ends on the circle, which is longest? Think about whether it passes through the centre.
Of all lines with both ends on the circle, the diameter through the centre is longest: 2 × 9 = 18.

7. B
Where does a radius start? Check whether each thick line starts at the centre O and ends on the circle.
A radius runs from the centre to any point on the circle.
8. C
Check each thick line: does it pass through the centre O, and are both its ends on the circle?
A diameter goes through the centre with both ends on the circle.
9. C. 3
Is the gap between the compass legs the radius or the diameter? Start from the 6 cm diameter.
The legs are opened to the radius: 6 ÷ 2 = 3.
10. True
Recall how the diameter and radius relate, work out the diameter for a 15 cm radius, then compare it with 30.
The diameter is twice the radius: 15 × 2.
11. B. 4
Is the gap between the compass legs the radius or the diameter? Start from the 8 cm diameter.
The legs are opened to the radius: 8 ÷ 2 = 4.
12. True
Recall how the diameter and radius relate, work out the diameter for a 20 cm radius, then compare it with 40.
The diameter is twice the radius: 20 × 2.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 210 cm
How much of the line does each coaster take up: its radius or its diameter? Work out one coaster's diameter first.
Each takes up a diameter, 2 × 15; 7 of them: 210 cm.
14. 4 cm
The biggest circle just touches all four sides. How does its diameter compare with the 8 cm side?
The biggest circle is 8 cm across, and the compasses open to the radius: 8 ÷ 2 = 4.
15. 18 m
Is edge to centre a radius or a diameter? Start from the pond's 36 m width.
Edge to centre is a radius: 36 ÷ 2 = 18 m.
16. 5 biscuits
Each biscuit takes 10 cm along and 10 cm across. Work out how many fit along the 50 cm side first; part of a biscuit doesn't count.
Each takes a 10 cm square: the whole number of 50 ÷ 10 along, of 16 ÷ 10 across, multiplied: 5.
17. 182 cm
How much of the line does each coaster take up: its radius or its diameter? Work out one coaster's diameter first.
Each takes up a diameter, 2 × 13; 7 of them: 182 cm.
18. 54 biscuits
Each biscuit takes 5 cm along and 5 cm across. Work out how many fit along the 47 cm side first; part of a biscuit doesn't count.
Each takes a 5 cm square: the whole number of 47 ÷ 5 along, of 31 ÷ 5 across, multiplied: 54.

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