Fraction of Circle: Challenge & Extension
Mathematics
GCSE Higher
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on calculating fractions of circles, including sector areas, with extension and challenge questions suitable for GCSE Higher students.
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Fraction of Circle: Challenge & Extension
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 sector with a central angle of 60° in a circle with radius 10 cm.
[3 marks]2.
Find the fraction of the circle's area that a sector with a 90° central angle represents in a circle of radius 7 cm.
[3 marks]3.
A sector with a 120° angle is cut from a circle with radius 15 cm. What is the area of the sector?
[4 marks]4.
Construct a sector with a 45° central angle and radius 8 cm on your grid. Calculate its area.
[4 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working in the grid spaces provided.
1.
A circular garden has a sector with a 150° central angle. If the radius of the garden is 12 meters, what is the area of this sector? Explain your method.
[5 marks]2.
The central angle of a sector is doubled. How does this affect the sector's area? Provide reasoning and calculations for initial and final areas.
[5 marks]3.
A wheel of radius 0.5 meters rotates through 90°. Calculate the length of the arc traveled by a point on the rim.
[4 marks]4.
A cake is cut into 8 equal sectors. If the radius of the cake is 20 cm, find the area of one sector. Then, determine what fraction of the whole cake this sector represents.
[4 marks]5.
Explain why sectors with the same central angle but different radii have areas proportional to the squares of their radii. Support your explanation with a calculation example.
[5 marks]C
Real-world Applications
Answer all questions. Provide calculations and reasoning.
1.
A wind turbine blade cuts a 90° sector from a circular disk of radius 5 meters. What is the area of the blade? How might this relate to real-world engineering?
[4 marks]2.
A circular track has a 60° bend. If the radius of the bend is 30 meters, find the length of the curved section. Discuss how this calculation might be useful in race track design.
[4 marks]D
Challenge & Extension
Tackle these more difficult problems. Show detailed working.
1.
A sector of a circle with radius 9 cm has an area of 45π cm². Find the size of the central angle in degrees. Show all steps.
[4 marks]2.
Design a sector with a central angle of 120° and radius 14 cm. Calculate its area and verify if it is exactly one-third of the total circle. Justify your answer.
[4 marks]E
Mixed Review & Error Analysis
Attempt all questions. Review your work carefully.
1.
A student calculated the sector area with a 45° angle and radius 12 cm as 50 cm². Identify and correct the mistake in their calculation.
[3 marks]2.
A sector with a 180° angle in a circle of radius 8 cm has an area calculated as 32π cm². Is this correct? Explain and correct if necessary.
[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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet