Fraction of Circle: Problem Solving & Reasoning
Mathematics
GCSE Higher
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the concept of calculating fractions of circles, including sector areas, with varied questions designed for GCSE Higher students.
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Fraction of Circle: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Review the key concept: the area of a sector is a fraction of the total circle's area, given by (θ/360) × πr², where θ is the angle in degrees.
B
Fluency & Practice
Answer the following procedural questions to build foundational skills.
1.
Calculate the area of a sector with a central angle of 60° in a circle of radius 10 cm.
[3 marks]2.
What fraction of a circle's area does a sector with a 90° angle represent?
[2 marks]3.
A circle has radius 15 cm. Find the area of the sector with a 120° central angle.
[3 marks]4.
Express the sector area as a fraction of the entire circle for an angle of 45° in a circle of radius 8 cm.
[2 marks]C
Problem Solving & Reasoning
Tackle these multi-step problems that require explanation and reasoning.
1.
A sector with a 90° angle is cut from a circle with radius 12 cm. Calculate its area and explain how the sector's size compares to the whole circle.
[4 marks]2.
A wheel of radius 0.5 meters turns through 135°. Find the length of the arc it traces and describe your method.
[4 marks]3.
Explain why the sector with a 180° angle is exactly half the area of the circle, including any assumptions.
[3 marks]D
Real-world Applications
Apply your understanding to practical contexts.
1.
A radar display shows a sector with a 45° central angle in a circular area of radius 20 km. Calculate the area of this sector and explain its relevance in navigation.
[4 marks]E
Challenge & Extension
Tackle these advanced problems and explore extensions of the concept.
1.
A sector with a 150° angle is cut from a circle with radius 9 cm. Find its area, and determine what fraction of the circle this sector represents. Show all steps.
[4 marks]2.
Construct a sector with a central angle of 100° and radius 7 cm. Using the grid, draw an approximate sector and label the key measurements.
[3 marks]F
Mixed Review & Error Analysis
Review different question types and identify common mistakes.
1.
A student calculates the sector area with a 60° angle and radius 10 cm as 50 cm². Identify the mistake and correct it.
[3 marks]2.
A sector with a 90° angle is mistakenly assumed to be one-quarter of the circle's area in a problem. Explain a common misconception that leads to this error and clarify the correct approach.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet