Segment: Problem Solving & Reasoning

Mathematics
Grade 8
14 questions
~28 mins
1 views0 downloads

About This Worksheet

A worksheet focusing on the concept of segments within circles, including calculations, reasoning, and real-world applications for Grade 8 students.

Worksheet Preview

Full preview • 14 questions

Segment: Problem Solving & Reasoning

Subject: MathematicsGrade: Grade 8
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz

Untitled Worksheet

Grade Grade 8
A

Fluency & Practice

Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the length of the chord if the radius of the circle is 10 cm and the corresponding segment subtends a 60° central angle.
[3 marks]
2.
Find the area of the segment formed when a 12 cm radius circle has a 90° segment.
[4 marks]
3.
If the height of a segment is 4 cm in a circle of radius 7 cm, what is the length of the chord?
[3 marks]
4.
Construct a segment with a chord length of 8 cm in a circle with radius 10 cm. Calculate the height of the segment.
[4 marks]
B

Problem Solving & Reasoning

Solve the following multi-step problems and explain your reasoning clearly.
1.
A circle has a radius of 15 cm. A segment subtends a 120° central angle. Calculate the area of this segment. Show all steps.
[6 marks]
2.
In a circle, a chord of length 14 cm subtends a segment with a height of 6 cm. Determine the radius of the circle. Explain your solution process.
[6 marks]
3.
A sector with a radius of 9 cm has a segment with a height of 4 cm. Find the angle subtended at the center by the sector.
[4 marks]
C

Real-world Applications

Apply your understanding of segments to the following real-world scenarios.
1.
A park is designed in the shape of a circle with a segment opening to a viewing platform. If the radius of the park is 50 meters and the segment subtends a 30° angle, calculate the area available for visitors in this segment.
[6 marks]
2.
A circular swimming pool has a segment that is used as a shallow lounging area. The radius of the pool is 8 meters, and the segment covers 45° of the circle. Find the length of the boundary of this lounging area.
[4 marks]
D

Challenge & Extension

Attempt these more advanced problems to extend your understanding.
1.
Construct a segment in a circle of radius 10 cm such that the segment's area is exactly 20 cm². Determine the height and the chord length, showing your methods.
[8 marks]
2.
Prove that the area of a segment approaches zero as the subtended angle approaches 0°, and approaches the area of the sector as the angle approaches 180°.
[8 marks]
E

Mixed Review

Solve a variety of problems to review your understanding of circle segments.
1.
A circle with radius 6 cm has a segment with a height of 2 cm. Calculate the length of the chord defining this segment.
[3 marks]
2.
In a circle, a segment subtends a 75° angle at the center. Find the length of the segment's chord if the radius is 9 cm.
[3 marks]
F

Error Analysis

Review the following common mistake and identify the correction needed.
1.
A student calculates the area of a segment using the sector area formula without subtracting the triangular portion. Explain why this is incorrect and how to properly find the segment area.
[4 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.

  • • Change grade level (Grade 6 → Grade 7)
  • • Swap topics (Harry Potter → Macbeth)
  • • Add more questions (10 → 15)
  • • Adjust difficulty

Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet