Class 10 Maths Chapter 11 Areas Related to Circles – Exercise 11.1 NCERT Solutions

Introduction

Exercise 11.1 introduces the basic formulas for areas and perimeters of circles. You’ll learn how to calculate the circumference and area of a circle, as well as solve problems involving semicircles and quadrants. This exercise builds the foundation for solving real‑life problems involving circular shapes.

Formula Used

1. Circumference of Circle:

$$C=2\pi r$$

2. Area of Circle:

$$A=\pi r^2$$

3. Area of Semicircle:

$$A=\frac{1}{2}\pi r^2$$

4. Area of Quadrant:

$$A=\frac{1}{4}\pi r^2$$

NCERT Questions with Solutions (10)

Q1. Find circumference of circle with radius 7 cm.

Solution: $C=2\pi r=2\times \frac{22}{7}\times 7=44\text{cm}$.

Q2. Find area of circle with radius 14 cm.

Solution: $A=\pi r^2=\frac{22}{7}\times 14\times 14=616{\text{cm}}^2$.

Q3. Find circumference of circle with diameter 10 cm.

Solution: Radius = 5 cm. $C=2\pi r=2\times \frac{22}{7}\times 5=\frac{220}{7}\text{cm}$.

Q4. Find area of circle with diameter 28 cm.

Solution: Radius = 14 cm. $A=\pi r^2=\frac{22}{7}\times 14\times 14=616{\text{cm}}^2$.

Q5. Find circumference of circle with radius 21 cm.

Solution: $C=2\pi r=2\times \frac{22}{7}\times 21=132\text{cm}$.

Q6. Find area of circle with radius 3.5 cm.

Solution: $A=\pi r^2=\frac{22}{7}\times 3.5\times 3.5=38.5{\text{cm}}^2$.

Q7. Find circumference of circle with radius 2.1 cm.

Solution: $C=2\pi r=2\times \frac{22}{7}\times 2.1=13.2\text{cm}$.

Q8. Find area of semicircle with radius 7 cm.

Solution: $A=\frac{1}{2}\pi r^2=\frac{1}{2}\times \frac{22}{7}\times 7\times 7=77{\text{cm}}^2$.

Q9. Find area of quadrant with radius 14 cm.

Solution: $A=\frac{1}{4}\pi r^2=\frac{1}{4}\times \frac{22}{7}\times 14\times 14=154{\text{cm}}^2$.

Q10. Find circumference of circle with diameter 42 cm.

Solution: Radius = 21 cm. $C=2\pi r=2\times \frac{22}{7}\times 21=132\text{cm}$.

FAQs (10 from NCERT)

1. Q: What is circumference of circle? A: Length of boundary of circle, $2\pi r$.

2. Q: What is area of circle? A: Space enclosed by circle, $\pi r^2$.

3. Q: What is semicircle? A: Half of circle.

4. Q: What is quadrant? A: One‑fourth of circle.

5. Q: What is diameter? A: Longest chord, twice radius.

6. Q: What is radius? A: Distance from center to boundary.

7. Q: What is π (pi)? A: Ratio of circumference to diameter, approx 3.1416 or 22/7.

8. Q: Can area be negative? A: No, area is always positive.

9. Q: Why is circle important? A: Used in geometry, design, and real‑life applications.

10. Q: Why is this exercise important? A: It builds foundation for solving problems involving circular shapes.

Conclusion

Exercise 11.1 has 10 solved questions and 10 FAQs that strengthen your understanding of circle area and circumference. This builds the foundation for advanced problems in areas related to circles in Class 10 Maths.

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New Syllabus- Class 10 Maths Chapter 11 Areas Related to Circles – Exercise 11.1 NCERT Solutions