A = πr²: Challenge & Extension
Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the formula for the area of a circle, A = πr², including procedural practice, problem solving, and extension questions for Year 9 students.
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A = πr²: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the area of a circle with radius 5 cm.
[2 marks]2.
A circle has an area of 50.24 cm². What is its radius? (Use π ≈ 3.14)
[3 marks]3.
Construct a circle with a radius of 3 cm. Calculate its area.
[3 marks]4.
A circular garden has a radius of 8 meters. Find its area.
[2 marks]B
Problem Solving & Reasoning
Answer all questions with clear working and explanations where appropriate.
1.
A circular swimming pool has an area of 150.8 m². Calculate its radius. (Use π ≈ 3.14).
[4 marks]2.
A metal disc has a radius of 10 cm. It is melted and reformed into a smaller disc with a radius of 5 cm. Has the amount of metal (area) increased, decreased, or stayed the same? Justify your answer.
[4 marks]3.
Explain why the area of a circle increases as the radius increases. Use the formula A = πr² in your explanation.
[3 marks]4.
A circular table has a diameter of 2 meters. Calculate the area of the tabletop.
[3 marks]C
Real-world Applications
Answer all questions with appropriate calculations and reasoning.
1.
A circular running track has a radius of 30 meters. Find the area of the track surface for the inner circle. If the track width is 2 meters, what is the total area of the outer circle? (Use π ≈ 3.14).
[4 marks]2.
A circular flower bed has a radius of 4 meters. The gardener wants to pave a path 1 meter wide around it. Calculate the area of the paved path.
[3 marks]D
Challenge & Extension
Attempt these more challenging questions. Show detailed working.
1.
A circle has an area of 113.1 cm². Find its radius with π ≈ 3.14. Then, find the circumference of the circle.
[4 marks]2.
Design a circle with an area exactly twice that of a circle with radius 3 cm. What is the radius of your new circle?
[4 marks]E
Mixed Review & Error Analysis
Answer the following questions to review your understanding. Pay attention to common mistakes.
1.
A student calculates the area of a circle with radius 4 cm as 50 cm². Identify the mistake and correct it.
[2 marks]2.
A circle with radius 7 cm is mistakenly thought to have an area of 100 cm². Explain the error and provide the correct area.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet