Geometry and measurement

Area of a Circle Practice

Use radius and diameter to find circle areas, compare scaled circles, and solve ring and composite-area problems with worked solutions.

Grades 7–8 practice · 6 questions · Free to print · Answers included

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Make sense of the method

Circle area measures the surface inside the boundary. Its formula is A = πr², where r is the radius.

Rearranging narrow circle sectors gives an approximate parallelogram with height r and base half the circumference, πr. This explains why the area is πr × r. Keep π in exact answers; use 3.14 only when a question requests it.

Find the radius. If a diameter is given, divide it by 2.
Square the radius before multiplying by π.
Use square units for area.
For a ring or a shape with a circular hole, subtract areas of whole regions.

A worked example

Find the area of a circle with radius 4 cm. Give an exact answer and an estimate using π ≈ 3.14.

Example circle

A = πr² = π × 4².
4² = 16, so A = 16π cm².
Using 3.14 gives 3.14 × 16 = 50.24 cm².

16π cm², approximately 50.24 cm².

Try the worksheet

Start with the first two questions, then build toward the final challenge. Show your method with calculations, drawings or a short explanation. These are practice questions with published answers, not a full-topic readiness check.

Build the foundation
1.A circle has radius 3 m. Find its area in terms of π and using π ≈ 3.14.
Radius given
Show your work on paper.
Build the foundation
2.A circular plate has diameter 14 cm. Find its area, exactly and using π ≈ 3.14.
Plate diameter
Show your work on paper.
Strengthen your method
3.A semicircular window has radius 5 cm. Find the area of the semicircle in terms of π and using 3.14.
Show your work on paper.
Strengthen your method
4.One circle has radius 2 cm and another has radius 6 cm. Find the ratio of their areas, larger to smaller, and explain why it is not 3:1.
Show your work on paper.
Apply and explain
5.A circular ring has outer radius 8 m and inner radius 5 m. Sketch concentric circles and find the ring area exactly and using 3.14.
Show your work on paper.
Apply and explain
6.A square of side 12 cm contains an inscribed circle touching all four sides. Sketch the figure and find the area inside the square but outside the circle, using π ≈ 3.14.
Show your work on paper.

Download free worksheetPDF

Worked answers

Try the questions first. Then compare the reasoning, not just the final result.

Show all six worked solutions

1. 9π m², approximately 28.26 m².
1. Square the radius: 3² = 9.
2. Multiply by π: A = 9π m².
3. Approximation: 9 × 3.14 = 28.26 m².
2. 49π cm², approximately 153.86 cm².
1. Radius = 14 ÷ 2 = 7 cm.
2. A = π × 7² = 49π cm².
3. 49 × 3.14 = 153.86 cm².
3. 12.5π cm², approximately 39.25 cm².
1. The complete circle has area π × 5² = 25π cm².
2. A semicircle has half that area: 25π ÷ 2 = 12.5π cm².
3. 12.5 × 3.14 = 39.25 cm².
4. The area ratio is 9:1.
1. Small area = 4π cm²; large area = 36π cm².
2. 36π ÷ 4π = 9.
3. The radius factor is 3, so the area factor is 3² = 9.
5. 39π m², approximately 122.46 m².
1. Outer disk: π × 8² = 64π m².
2. Inner disk: π × 5² = 25π m².
3. Subtract disk areas: 64π − 25π = 39π m², approximately 122.46 m².
4. Squaring the radius difference would give the area of a different circle, not the ring.
6. 30.96 cm².
1. Square area = 12 × 12 = 144 cm².
2. The circle diameter is 12 cm, so its radius is 6 cm.
3. Circle area ≈ 3.14 × 6² = 113.04 cm².
4. Outside area ≈ 144 − 113.04 = 30.96 cm².

Mistakes worth catching

Putting the diameter into πr².

Halve the diameter first. Using it as the radius makes area four times too large.

Writing centimetres instead of square centimetres.

Area counts surface units, so use cm² or another square unit.

Finding ring area from the difference of radii.

Calculate the two disk areas and subtract them.

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Skills covered

Geometry and measurement

Calculate circle areas from a radius or diameter.
Apply area reasoning to rings, scaled circles and composite shapes.

Choose this practice by the skills you need. Grade placement and strand names vary between school systems; one worksheet covers selected skills rather than every expectation in a topic.

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Area of a Circle Practice

Make sense of the method

A worked example

Try the worksheet

1.A circle has radius 3 m. Find its area in terms of π and using π ≈ 3.14.

2.A circular plate has diameter 14 cm. Find its area, exactly and using π ≈ 3.14.

3.A semicircular window has radius 5 cm. Find the area of the semicircle in terms of π and using 3.14.

4.One circle has radius 2 cm and another has radius 6 cm. Find the ratio of their areas, larger to smaller, and explain why it is not 3:1.

5.A circular ring has outer radius 8 m and inner radius 5 m. Sketch concentric circles and find the ring area exactly and using 3.14.

6.A square of side 12 cm contains an inscribed circle touching all four sides. Sketch the figure and find the area inside the square but outside the circle, using π ≈ 3.14.

Worked answers

1. 9π m², approximately 28.26 m².

2. 49π cm², approximately 153.86 cm².

3. 12.5π cm², approximately 39.25 cm².

4. The area ratio is 9:1.

5. 39π m², approximately 122.46 m².

6. 30.96 cm².