C = πd: Error Analysis & Misconceptions
Mathematics
Grade 8
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding, applying, and correcting misconceptions related to the formula C = πd for the circumference of a circle.
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C = πd: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the circumference of a circle with a diameter of 12 cm.
[2 marks]2.
A circle has a diameter of 20 meters. What is its circumference? (Use π ≈ 3.14)
[2 marks]3.
If the circumference of a circle is 31.4 cm, find its diameter.
[2 marks]4.
A bicycle wheel has a diameter of 70 inches. Calculate its circumference.
[2 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems. Show all workings.
1.
A circular garden has a diameter of 15 meters. A gardener plants a flower bed along the edge. If the gardener mistakenly uses a diameter of 20 meters in the calculation, what is the difference between the correct and incorrect circumference?
[4 marks]2.
A circular pool has a circumference of 94.2 meters. What is its diameter? Use π ≈ 3.14.
[3 marks]3.
A circular track has a diameter of 100 meters. If a runner runs 314 meters along the track, how many times around the track has the runner completed? (Use π ≈ 3.14)
[3 marks]C
Real-world Applications
Apply your understanding to the following word problems.
1.
A engineering company designs circular cables with a diameter of 5 cm. How much cable length is needed to create 10 such cables? (Use π ≈ 3.14)
[3 marks]2.
A circular track has a circumference of 400 meters. A runner trains on this track but mistakenly uses a diameter of 130 meters in their calculations. Find the mistake in the runner’s estimated diameter if they assumed the diameter was correct, and what the actual diameter is based on the circumference.
[4 marks]D
Challenge & Extension
Attempt these advanced problems to deepen your understanding.
1.
A circular mirror has a diameter of 60 cm. If a crack causes the diameter to be misread as 55 cm, what is the percentage error in the calculated circumference?
[3 marks]2.
Design a circle on the grid with a diameter of 8 units. Show the steps to find its circumference and verify if students can accurately apply C=πd.
[4 marks]E
Mixed Review & Error Analysis
Identify and correct the errors in the following questions.
1.
A circular fountain has a diameter of 18 meters. A student incorrectly calculates the circumference using C = 2πr instead of C = πd. Find the student's answer and identify the mistake.
[3 marks]2.
A circle's diameter is given as 25 units. A student calculates the circumference as 125 units. Is this correct? Explain and correct if necessary.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet