Class 10 Maths Chapter 11 Areas Related to Circles – Exercise 11.2 NCERT Solutions

Introduction

Exercise 11.2 focuses on areas of sectors and segments of a circle. These problems involve calculating the area enclosed by an arc (sector) and the area bounded by a chord and arc (segment). This exercise builds your ability to apply circle area formulas to practical problems.

Formula Used

1. Area of Sector (θ in degrees):

$$A=\frac{\theta }{{360}^{\circ }}\cdot \pi r^2$$

2. Length of Arc (θ in degrees):

$$L=\frac{\theta }{{360}^{\circ }}\cdot 2\pi r$$

3. Area of Segment:

$$A=\text{Area of sector}-\text{Area of triangle}$$

NCERT Questions with Solutions (10)

Q1. Find area of sector of circle with radius 7 cm and angle 90°.

Solution: $A=\frac{90}{360}\cdot \pi \cdot 7^2=\frac{1}{4}\cdot \frac{22}{7}\cdot 49=38.5{\text{cm}}^2$.

Q2. Find length of arc of circle with radius 14 cm and angle 60°.

Solution: $L=\frac{60}{360}\cdot 2\pi \cdot 14=\frac{1}{6}\cdot 28\pi =\frac{88}{6}=14.67\text{cm}$.

Q3. Find area of sector of circle with radius 21 cm and angle 120°.

Solution: $A=\frac{120}{360}\cdot \pi \cdot {21}^2=\frac{1}{3}\cdot \frac{22}{7}\cdot 441=462{\text{cm}}^2$.

Q4. Find length of arc of circle with radius 10 cm and angle 45°.

Solution: $L=\frac{45}{360}\cdot 2\pi \cdot 10=\frac{1}{8}\cdot 20\pi =\frac{20\pi }{8}=7.85\text{cm}$.

Q5. Find area of sector of circle with radius 14 cm and angle 150°.

Solution: $A=\frac{150}{360}\cdot \pi \cdot {14}^2=\frac{5}{12}\cdot \frac{22}{7}\cdot 196=458.3{\text{cm}}^2$.

Q6. Find length of arc of circle with radius 7 cm and angle 135°.

Solution: $L=\frac{135}{360}\cdot 2\pi \cdot 7=\frac{3}{8}\cdot 14\pi =\frac{42\pi }{8}=16.5\text{cm}$.

Q7. Find area of sector of circle with radius 6 cm and angle 60°.

Solution: $A=\frac{60}{360}\cdot \pi \cdot 6^2=\frac{1}{6}\cdot \pi \cdot 36=18.85{\text{cm}}^2$.

Q8. Find length of arc of circle with radius 12 cm and angle 90°.

Solution: $L=\frac{90}{360}\cdot 2\pi \cdot 12=\frac{1}{4}\cdot 24\pi =18.85\text{cm}$.

Q9. Find area of sector of circle with radius 10 cm and angle 72°.

Solution: $A=\frac{72}{360}\cdot \pi \cdot {10}^2=\frac{1}{5}\cdot 100\pi =62.8{\text{cm}}^2$.

Q10. Find length of arc of circle with radius 15 cm and angle 150°.

Solution: $L=\frac{150}{360}\cdot 2\pi \cdot 15=\frac{5}{12}\cdot 30\pi =39.27\text{cm}$.

FAQs (10 from NCERT)

1. Q: What is sector of circle? A: Region enclosed by two radii and arc.

2. Q: What is segment of circle? A: Region enclosed by chord and arc.

3. Q: What is arc length formula? A: $\frac{\theta }{360}\cdot 2\pi r$.

4. Q: What is area of sector formula? A: $\frac{\theta }{360}\cdot \pi r^2$.

5. Q: What is minor sector? A: Smaller region formed by arc and radii.

6. Q: What is major sector? A: Larger region formed by arc and radii.

7. Q: What is minor segment? A: Smaller region formed by chord and arc.

8. Q: What is major segment? A: Larger region formed by chord and arc.

9. Q: Can angle be in radians? A: Yes, formulas can be adapted for radians.

10. Q: Why is this exercise important? A: It builds skills in calculating areas and lengths in circular geometry.

Conclusion

Exercise 11.2 has 10 solved questions and 10 FAQs that strengthen your understanding of areas of sectors and segments of circles. This builds the foundation for advanced problems in Class 10 Maths.

Visit: www.fuzymathacademy.com

New Syllabus-Class 10 Maths Chapter 11 Areas Related to Circles – Exercise 11.2 NCERT Solutions