Year 8 - Circles - Free practice

Year 8 Circles Worksheets & Practice Tests

Q: How do you find the circumference and area of a circle?

Use the formulas C = 2π r (or π d) for circumference and A = π r² for area, where r is the radius and d is the diameter. For example, a circle with radius 5 cm has circumference 2π(5) ≈ 31.42 cm and area π(5)² ≈ 78.54 cm².

Area and circumference - the full Year 8 circle skill set.

Quick answer

How do you find the circumference and area of a circle?

Use the formulas $C = 2\pi r$ (or $\pi d$ ) for circumference and $A = \pi r^2$ for area, where $r$ is the radius and $d$ is the diameter. For example, a circle with radius 5 cm has circumference $2\pi(5) \approx 31.42$ cm and area $\pi(5)^2 \approx 78.54$ cm².

Generate a free maths worksheet

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

Want more than a worksheet?

Practice built from mistakes.

A worksheet on Year 8 circles is a good start. Tuterly goes further: it turns any question students get wrong into fresh practice, at the right level, on what’s likely to be in the next test or exam.

~90% of Bayside Academics students using it weekly improved their test marks

Of the Bayside Academics students who used Tuterly at least once a week, about 90% improved their school test marks.

Based on the actual school test marks of 100+ Bayside Academics students (in person and online) in Years 7 to 10, before and after using Tuterly at least once a week. How we measured this

Free worksheet Tuterly

The questionsFree worksheetThe same questions for every student on this topic.TuterlyWritten from the questions they got wrong in homework and school tests, at their level.

How manyFree worksheetOne sheet at a time.TuterlyAs many fresh questions as they need, each one different, never just the numbers swapped.*

Before a testFree worksheetPick a topic and hope it’s the right one.TuterlyA practice test covering every part of the topic. Upload the term planner and it focuses on what’s coming up.

MarkingFree worksheetCheck the answer key yourself.TuterlyMarked as they go, with the exact step that went wrong explained.

ProgressFree worksheetNothing is saved.TuterlyEvery question tracked until it’s mastered, and a weekly review for parents.

For Years 7 to 10: $8.99 a week or $29.99 a month at the launch price (from 1 April 2027, $17.99 a week or $59.99 a month), with a 7-day free trial on the monthly plan only. Better marks in 6 months, or your money back.

Or try it free now on one of their questions →

Coming soon on iPhone. Android soon after.

Free to download · 7-day free trial on monthly · Years 7 to 10 maths · On iPhone. Android coming soon

* With a subscription. Fair use applies: up to 80 snapped questions and 120 new practice questions a day per student.

Worked examples

Year 8 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 · Circumference and area from a radius
A circle has a radius of $9$ cm. Find its circumference and area. Give both answers correct to one decimal place.
Show worked solution
Key idea: Circumference $C = 2\pi r$ and area $A = \pi r^2$ , where $r$ is the radius.
1. Write the radius: $r = 9$ cm.
2. Find the circumference:
  $C = 2\pi r = 2 \times \pi \times 9 = 18\pi \approx 56.5 \text{ cm}$
3. Find the area:
  $A = \pi r^2 = \pi \times 9^2 = 81\pi \approx 254.5 \text{ cm}^2$
Answer: Circumference $\approx 56.5$ cm, Area $\approx 254.5$ cm $^2$
Example 2 · Area of a composite shape (semicircle and rectangle)
A shape is made from a rectangle and a semicircle. The rectangle is $10$ cm long and $6$ cm wide. The semicircle sits on top of one of the $6$ cm sides, with that side as its diameter. Find the total area of the shape, correct to one decimal place.
Show worked solution
Key idea: The total area is the area of the rectangle plus the area of the semicircle. The semicircle has diameter $6$ cm, so its radius is $3$ cm.
1. Find the radius of the semicircle: $r = 6 \div 2 = 3$ cm.
2. Find the area of the rectangle:
  $A_{\text{rect}} = 10 \times 6 = 60 \text{ cm}^2$
3. Find the area of the semicircle:
  $A_{\text{semi}} = \frac{1}{2}\pi r^2 = \frac{1}{2} \times \pi \times 3^2 = \frac{9\pi}{2} \approx 14.1 \text{ cm}^2$
4. Add the areas:
  $A_{\text{total}} = 60 + 14.1 = 74.1 \text{ cm}^2$
Answer: Total area $\approx 74.1$ cm $^2$
Example 3 · Real-world problem: circular garden border
A gardener wants to put a circular garden bed in a park. The garden bed has a radius of $3$ m, and there is a circular path $1$ m wide that runs around the outside of it, forming a larger circle with radius $4$ m. The garden bed will be planted with flowers, and the path will be paved. Find the area of the path only, correct to two decimal places.
Show worked solution
Key idea: The path is an annulus (a ring shape). Its area equals the area of the large circle minus the area of the small circle.
1. Write the radii: outer radius $R = 4$ m, inner radius $r = 3$ m.
2. Find the area of the large circle:
  $A_{\text{large}} = \pi R^2 = \pi \times 4^2 = 16\pi \text{ m}^2$
3. Find the area of the small circle:
  $A_{\text{small}} = \pi r^2 = \pi \times 3^2 = 9\pi \text{ m}^2$
4. Find the area of the path:
  $A_{\text{path}} = 16\pi - 9\pi = 7\pi \approx 21.99 \text{ m}^2$
Answer: The area of the path is $\approx 21.99$ m $^2$

Common mistakes

Where students usually lose marks

Confusing radius and diameter

Diameter $= 10$ cm, so $A = \pi \times 10^2 = 100\pi$ cm $^2$

Always halve the diameter before substituting into $A = \pi r^2$ or $C = 2\pi r$ . Here $r = 5$ cm, so $A = \pi \times 5^2 = 25\pi$ cm $^2$ .

Forgetting to square the radius when finding area

$A = \pi \times 6 = 6\pi$ cm $^2$ (with $r = 6$ cm)

The area formula is $A = \pi r^2$ , so you must square $r$ first. With $r = 6$ cm: $A = \pi \times 6^2 = 36\pi$ cm $^2$ .

Using the wrong fraction for a semicircle or quadrant

Area of a quadrant $= \frac{1}{2}\pi r^2$

A semicircle is half a circle ( $\frac{1}{2}\pi r^2$ ) and a quadrant is a quarter of a circle ( $\frac{1}{4}\pi r^2$ ). Always think about what fraction of the full circle you have.

Subtracting areas the wrong way around for an annulus

Area of annulus $= \pi r_{\text{small}}^2 - \pi R_{\text{large}}^2$

Always subtract the smaller (inner) area from the larger (outer) area: $A = \pi R^2 - \pi r^2$ . Doing it backwards gives a negative answer, which is impossible for an area.

Try one yourself

Your turn

A circular garden has a diameter of 8 m. What is the area of the garden in square metres, correct to 2 decimal places?

Got a different circles question wrong? Upload it to Tuterly and get the worked solution and a fresh one to practise, free.

About this worksheet

Why we built it

Year 8 is where students apply pi to both circumference and area of circles, and start handling composite shapes (semicircles, quadrants, annulus). These worksheets give your student practice on each variation - exact, decimal and word-problem answers - so the formulas stay in long-term memory.

What's covered

Sub-skills your student will practise

✓Circumference using diameter or radius
✓Area of a circle from radius or diameter
✓Working back from an area or circumference to find the radius
✓Composite shapes (semicircles, quadrants, annulus)
✓Real-world circle problems (running tracks, gardens, pizzas)

From our families

Parents on the practice questions.

“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”

Rebecca M.

Year 8 · Maths

“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”

Priya S.

Year 9 · Maths

“I like that I can just keep doing questions until it clicks. If I get something wrong, it shows me why, and then gives me another one like it.”

Ella, student

Year 10 · Maths

Verified parent

Frequently asked

Questions parents ask about circles

What's the difference between circumference and area of a circle?

Circumference is the distance around the circle (the perimeter). Area is the space inside. Different formulas: C = pi x d for circumference, A = pi x r^2 for area.

Why is the area formula pi r squared?

If you imagine slicing a circle into thin wedges and rearranging them, they approximate a rectangle with height equal to the radius and width equal to half the circumference. So area = r x (1/2 x 2 x pi x r) = pi x r^2.

What does Year 8 do with composite shapes?

Year 8 introduces composite shapes like semicircles, quadrants, and annulus (a ring shape). Students learn to add and subtract circle parts from rectangles or each other - a key skill for SAC questions.

Are exact (in terms of pi) answers acceptable?

Yes - many Year 8 questions specifically ask for an exact answer in terms of pi (e.g., 16 pi cm^2). Decimal answers are also accepted, usually to 1 or 2 decimal places.

Better maths marks start with the next wrong answer.

Tuterly turns every missed maths question into practice tailored towards the student, not just a generic worksheet.