Year 7 - Circles - Free practice

Year 7 Circles Worksheets & Practice Tests

Pi, circumference, radius and diameter - all the early-circle work.

Quick answer

How do you calculate the circumference of a circle?

The circumference of a circle equals pi times the diameter: C = πd, or equivalently C = 2πr. Pi (π ≈ 3.14159) is the ratio of any circle's circumference to its diameter. For example, a circle with radius 5 cm has circumference 2 × π × 5 ≈ 31.42 cm.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 7 circles: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Calculating circumference from diameter
A circle has a diameter of $10$ cm. Calculate its circumference. Use $\pi \approx 3.14$ and give your answer rounded to one decimal place.
Show worked solution
Key idea: The circumference of a circle is $C = \pi d$ , where $d$ is the diameter.
1. Write the formula: $C = \pi d$
2. Substitute $d = 10$ and $\pi \approx 3.14$ :
  $C = 3.14 \times 10$
3. Calculate:
  $C = 31.4 \text{ cm}$
Answer: The circumference is $31.4$ cm.
Example 2 · Finding radius from circumference
A circle has a circumference of $94.2$ cm. Find its radius. Use $\pi \approx 3.14$ .
Show worked solution
Key idea: Use $C = 2\pi r$ and rearrange to find $r$ .
1. Write the formula: $C = 2\pi r$
2. Rearrange to make $r$ the subject:
  $r = \frac{C}{2\pi}$
3. Substitute $C = 94.2$ and $\pi \approx 3.14$ :
  $r = \frac{94.2}{2 \times 3.14} = \frac{94.2}{6.28}$
4. Calculate:
  $r = 15 \text{ cm}$
Answer: The radius is $15$ cm.
Example 3 · Distance travelled by a rolling wheel
Aisha rides her bike to school. Each wheel on her bike has a diameter of $60$ cm. The school is $1{,}884$ m away. How many full rotations does each wheel make on the trip to school? Use $\pi \approx 3.14$ .
Show worked solution
Key idea: Each time a wheel makes one full rotation, it travels a distance equal to its circumference. Divide the total distance by the circumference to find the number of rotations.
1. Find the circumference of the wheel:
  $C = \pi d = 3.14 \times 60 = 188.4 \text{ cm}$
2. Convert the distance to school into centimetres:
  $1{,}884 \text{ m} = 188{,}400 \text{ cm}$
3. Divide the total distance by the circumference:
  $\text{Rotations} = \frac{188{,}400}{188.4} = 1{,}000$
Answer: Each wheel makes $1{,}000$ full rotations.

Common mistakes

Where students usually lose marks

Mixing up radius and diameter

Diameter = 10 cm, so $C = 2 \times 3.14 \times 10 = 62.8$ cm (using the diameter as if it were the radius).

Always check which measurement you have been given. If you have the diameter, use $C = \pi d$ . If you have the radius, use $C = 2\pi r$ . Remember that the diameter is twice the radius, so $d = 2r$ .

Rounding pi too early

$\pi \approx 3$ (rounded too soon), giving $C = 3 \times 8 = 24$ cm instead of $25.1$ cm.

Only round your final answer, not $\pi$ itself mid-calculation. Use the value of $\pi$ given in the question (such as $3.14$ ) all the way through, and round only at the very last step.

Forgetting to convert units

Diameter = 50 cm, distance = 500 m, so rotations $= 500 \div 157 = 3.18\ldots$ (mixing metres and centimetres).

Before dividing, make sure the circumference and the total distance are in the same units. Convert everything to centimetres or everything to metres before you calculate.

Dividing by π instead of 2π when finding the radius

$r = \frac{C}{\pi} = \frac{62.8}{3.14} = 20$ cm (this actually gives the diameter, not the radius).

The formula is $C = 2\pi r$ , so rearranging gives $r = \dfrac{C}{2\pi}$ . Do not forget the factor of $2$ . If you use this formula and get a suspiciously large answer, check whether you accidentally found the diameter.

Try one yourself

Your turn

A circular garden bed has a diameter of 8 m. What is its circumference, correct to 2 decimal places? Give your answer in metres.

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About this worksheet

Why we built it

Year 7 is where students meet pi formally for the first time. These worksheets keep things at the right level: relating radius, diameter and circumference, with a few applied problems thrown in. (Area of a circle is mostly Year 8 - check the Year 8 worksheets when you get there.)

What's covered

Sub-skills your student will practise

✓Relationship between diameter and radius
✓Pi as the ratio of circumference to diameter
✓Calculating circumference given the radius or diameter
✓Working back from circumference to find the radius
✓Mixed circle word problems (wheels, tracks, gardens)

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Frequently asked

Questions parents ask about circles

Why is pi about 3.14?

Pi is the ratio of any circle's circumference to its diameter - it's the same number no matter how big or small the circle is. The actual value never terminates or repeats, so 3.14 (or 22/7) is a working approximation.

What circle formulas does Year 7 use?

Year 7 covers the circumference (C = pi x diameter or 2 x pi x radius). Area of a circle is mostly a Year 8 topic and isn't required at Year 7 level.

How do students decide whether to use diameter or radius?

Whichever the question gives. If only the radius is given, double it for the diameter. C = pi x d and C = 2 x pi x r are the same formula written two ways.

Why might my child's answer not match the textbook exactly?

Because of how pi is rounded. If the textbook uses pi = 3.14 and your child used 3.14159, answers will differ slightly. Most school assessments accept either as long as the working is shown.

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