Chapter 11 · Class X Mathematics · NCERT Exercises

Areas Related to Circles — Exercises

Sector · Segment · Combined Figures — 35 Area Problems Solved

📂 3 Exercises 📝 26 Questions 🎓 Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

Perimeter and area of circle; circumference; basic sector and segment

Area of sector; area of minor/major segment; combined figures

Complex shaded regions; square/circle combinations; quadrant problems

3 exercise files · 26 total questions

Chapter at a Glance

CBSE BoardsNTSE

8 Concepts

10 Formulas

Moderate Difficulty

6–7% Weightage

Before You Begin

Prerequisites

✓Area of triangles and quadrilaterals
✓Circle basics
✓Pythagoras (for segment area)

Have Ready

🔧π = 22/7 or 3.14 as instructed
🔧Calculator
🔧Coloured pencils for shaded region identification

Exercise Topic Map

Exercise 11.1 Circumference = 2πr; Area = πr²; Arc length = (θ/360°)×2πr

Exercise 11.2 Sector area = (θ/360°)×πr²; Segment = Sector area − Triangle area; use standard values for triangle if θ = 60°,90°,120°

Miscellaneous Identify shaded region = (larger shape) − (inner shapes); work systematically with exact π form until last step

Key Formulae — Recall Before Solving

\(\text{Area of sector} = \dfrac{\theta}{360°} \times \pi r^2\)

\(\text{Arc length} = \dfrac{\theta}{360°} \times 2\pi r\)

\(\text{Segment area} = \text{Sector area} - \text{Area of }\triangle\)

\(\text{Area of equilateral }\triangle = \dfrac{\sqrt{3}}{4}a^2;\quad \text{right }\triangle = \tfrac{1}{2}bh\)

NCERT Solving Method

Step 1 — Shade or label each region in the figure before computing. Step 2 — Segment: always compute sector area and triangle area separately; subtract. Step 3 — Triangle area in segment: for θ=60°, use equilateral formula; for θ=90°, use ½r²; for others use ½r²sinθ. Step 4 — Keep π as fraction until the final numerical answer; avoids accumulated rounding errors.

Continue Your Preparation

📖NotesTheory & concepts 🧠MCQsTopic-wise practice ⚖️True–FalseConcept check ➡️Next ChapterSurface Areas and Volumes

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