C = 2πr: Real-world Applications
Mathematics
Year 9
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the formula C = 2πr through real-world applications, practice questions, and reasoning tasks for Year 9 students.
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C = 2πr: Real-world Applications
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 circumference of a circle with a radius of 7 cm.
[2 marks]2.
A circular garden has a diameter of 12 meters. What is its circumference? (Use π ≈ 3.14)
[2 marks]3.
Find the radius of a wheel if its circumference is 94.2 meters.
[2 marks]4.
Calculate the circumference of a circle with a radius of 3.5 meters.
[2 marks]B
Problem Solving & Reasoning
Answer the following multi-step questions, showing all working.
1.
A swimming pool has a circular shape with a radius of 10 meters. The pool cover is placed on top and needs a new cover with a circumference of 62.8 meters. What is the radius of the cover? Is it larger or smaller than the pool's radius? Show your reasoning.
[4 marks]2.
A race track is in the shape of a perfect circle with a circumference of 400 meters. A runner completes 5 laps. How far has the runner traveled? Show your calculations.
[3 marks]C
Real-world Applications
Solve these problems based on real-life scenarios.
1.
A bicycle wheel has a radius of 0.35 meters. How many revolutions does it make in traveling 1 km? (Use π ≈ 3.14).
[3 marks]2.
A circular running track has a circumference of 400 meters. If a runner runs 3 laps, what is the total distance? Provide reasoning.
[3 marks]D
Challenge & Extension
Attempt these more difficult questions to extend your understanding.
1.
A circular fountain has a diameter of 5 meters. A statue is placed exactly at the center. Calculate the length of fencing needed to surround the fountain if the fence runs along the circle's edge. Now, if the diameter is increased by 20%, what is the new length of fencing? Show all steps.
[4 marks]2.
Design a circle with a radius such that its circumference is exactly twice that of a circle with radius 4 meters. Explain your reasoning and calculations.
[4 marks]E
Mixed Review
Answer these questions to review your understanding of C = 2πr.
1.
Plot the graph of y = 2x for x between 0 and 10. How could this relate to calculating circumferences for circles with radii from 0 to 10?
[2 marks]2.
Construct a circle with a radius of 6 units on the grid. Then, draw another circle with a radius 50% larger. Calculate their circumferences and compare.
[4 marks]F
Error Analysis
Identify the mistake in the following problem and correct it.
1.
A student calculates the circumference of a circle with radius 5 cm as 10π cm, but writes the answer as 31.4 cm. Is this correct? If not, what mistake was made?
[2 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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet