A = πr²: Error Analysis & Misconceptions
Mathematics
GCSE Higher
12 questions
~24 mins
1 views0 downloads
About This Worksheet
This worksheet explores the area formula A = πr², focusing on common errors and misconceptions through varied question types.
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A = πr²: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
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. Express your answer in square centimeters.
[2 marks]2.
A circle has an area of approximately 113.1 cm². Find its radius, rounded to one decimal place.
[2 marks]3.
If the radius of a circle is doubled, what is the new area in terms of the original? Write your answer as a multiple of the original area.
[3 marks]B
Problem Solving & Reasoning
Answer all questions with detailed reasoning where applicable.
1.
A circular garden has an area of 50 m². A new pathway is added, reducing the usable area by 20%. Find the new radius of the garden in meters.
[4 marks]2.
Explain why using the formula A = 2πr instead of A = πr² is incorrect for calculating the area of a circle.
[3 marks]3.
A semi-circular pond has a radius of 4 meters. Calculate its total area.
[3 marks]C
Real-world Applications
Answer all questions in context.
1.
A designer is creating a circular table with a surface area of 0.5 m². What should be the radius of the table in centimeters?
[3 marks]2.
A circular swimming pool has a radius of 8 meters. If the pool's area is miscalculated as 150 m², identify the mistake and provide the correct area.
[4 marks]D
Challenge & Extension
Attempt these advanced questions to deepen your understanding.
1.
Prove that the ratio of areas of two circles is the square of the ratio of their radii.
[4 marks]2.
A circle's area is written as A = πr², but a student forgets to square the radius when calculating. If they use r = 7, what is their incorrect area estimate, and how does it compare to the correct?
[3 marks]E
Mixed Review & Error Analysis
Identify and correct the errors in each question.
1.
A student calculates the area of a circle with radius 10 cm as 314 cm², using π ≈ 3.14. They then mistakenly state that doubling the radius will double the area. Identify the mistake and correct the statement.
[4 marks]2.
The formula used was A = πr, instead of A = πr². Why does this lead to an incorrect calculation of the area?
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet