A free printable circles worksheet for Grade 8 math.
By Kris Reddy, Ontario teacher · Updated October 16, 2026 · 25 questions (30 marks) · PDF + answer key
This free area and circumference of a circle worksheet gives Grade 8 students complete practice with circles, from naming the parts to solving real-world problems. Students label the centre, radius, diameter and circumference, switch between radius and diameter, then find the circumference and area of eight drawn circles.
The second page stretches their thinking: working backwards from a circumference or area, finding the area and perimeter of a semicircle, finding the leftover area when a circle is cut from a square, and solving problems about a bike wheel, pizza sizes and a lawn sprinkler. Every answer uses π ≈ 3.14 and was checked by computer. To print it, use the Download button above.
| Part | Skill practised | Marks |
|---|---|---|
| A | Parts of a circle (labelled diagram) | 2 |
| B | Radius and diameter | 4 |
| C | Circumference of 4 drawn circles | 4 |
| D | Area of 4 drawn circles | 4 |
| E | Work backwards from C or A | 4 |
| F | Composite shapes (semicircle, circle in a square) | 4 |
| G | Three real-world problems | 6 |
| H | Spot the mistake | 2 |
The area and circumference of a circle worksheet supports the Ontario Grade 8 math curriculum in the Spatial Sense strand, where students develop and use the formulas for the circumference and area of a circle and solve related problems.
The radius goes from the centre to the edge. The diameter goes all the way across through the centre, so it is always twice the radius (d = 2r). The circumference is the distance around the circle. Part B of the worksheet practises switching between radius and diameter, including decimals like 5.6 cm and 12.5 mm.
For every circle, the circumference is a little more than 3 times the diameter. That number is π (pi), about 3.14:
C = πd or C = 2πr
Choose the version that matches what you're given. With a radius of 5 cm, C = 2 × 3.14 × 5 = 31.4 cm. Part C of this area and circumference of a circle worksheet mixes radii and diameters so students have to read each diagram carefully. For the history of π, see pi on Wikipedia.
The area is the space inside the circle, measured in square units:
A = πr²
The most common mistake is using the diameter. If a circle has a diameter of 10 m, first halve it: r = 5 m, so A = 3.14 × 25 = 78.5 m². Using 10 instead would give 314 m², four times too big. Part D of the area and circumference of a circle worksheet includes two diameter questions to catch this.
Once students know both formulas, they can run them in reverse. If C = 47.1 cm, then d = 47.1 ÷ 3.14 = 15 cm. If A = 314 m², then r² = 314 ÷ 3.14 = 100, so r = 10 m. That last step uses square roots; see the square roots worksheet for practice.
Composite shapes combine circles with other shapes. A semicircle's area is half a circle's, but its perimeter is half the circumference plus the diameter, which students often forget. And the shaded corners left when a 10 cm circle is cut from a 10 cm square have an area of 100 − 78.5 = 21.5 cm².
These questions match the area and circumference of a circle worksheet PDF, which has every circle drawn with its radius or diameter marked.
Open each part to check the area and circumference of a circle worksheet answers. All answers use π ≈ 3.14 and are rounded to one decimal place. The printable key is on the last two pages of the PDF.
These are the errors that come up most when marking this circle worksheet. Part H targets two of them directly.
For more practice, try the geometry shapes and properties quiz and the multi-step word problems quiz.
Yes. The worksheet and its answer key are free to download and print as one PDF, with no account needed.
C = πd, where d is the diameter. You can also use C = 2πr, since the diameter is twice the radius. A circle with diameter 12 m has C = 3.14 × 12 ≈ 37.7 m.
A = πr², where r is the radius. A circle with radius 4 cm has A = 3.14 × 4² = 3.14 × 16 ≈ 50.2 cm².
The formula A = πr² is built on the radius. If you're given the diameter, halve it first. Using the diameter by mistake makes the answer four times too big.
It is written for Grade 8 math and also works as Grade 9 review. All answers use π ≈ 3.14, rounded to one decimal.
Ready to start? Use the Download button above to print the free area and circumference of a circle worksheet double-sided, and keep the answer key pages for marking.