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CBSE Class 10 Maths Chapter 11: Areas Related to Circles Notes

📖 Chapter Notes ✏️ NCERT Solutions 📥 PDF Notes

1. Perimeter and Area of a Circle

2. Sector of a Circle and Its Area

A sector is the region enclosed by two radii and an arc of a circle (like a slice of pizza). If the angle at the center is $\theta$:

👉 Area of the Sector of angle $\theta$: $$\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2$$
👉 Length of an Arc of a sector of angle $\theta$: $$\text{Length} = \frac{\theta}{360^\circ} \times 2\pi r$$

3. Segment of a Circle and Its Area

A segment is the region enclosed by a chord and an arc. To find its area, you take the pizza slice (sector) and subtract the inner triangle:

$$\text{Area of Segment} = \text{Area of Sector} - \text{Area of Corresponding Triangle}$$
CBSE Clock-Hand Trick Question

Important Shortcut: Board exams love asking about the area swept by a minute hand of a clock in 5 minutes. Remember this conversion factor: The minute hand of a clock turns exactly $6^\circ$ in 1 minute. So, in 5 minutes, the center angle $\theta = 5 \times 6^\circ = 30^\circ$.

✏️ Complete NCERT Solutions Class 10 Areas Related to Circles

Exercise 11.1 (Rationalized Syllabus)
Q1. Find the area of a sector of a circle with radius $6\text{ cm}$ if angle of the sector is $60^\circ$.
Step 1: Identify given components
Radius $r = 6\text{ cm}$, Angle $\theta = 60^\circ$
Step 2: Plug into Area of Sector formula
$\text{Area} = \frac{60}{360} \times \pi \times 6^2$
Step 3: Solve algebraically (Take $\pi = 22/7$)
$\text{Area} = \frac{1}{6} \times \frac{22}{7} \times 36 = \frac{22 \times 6}{7} = \mathbf{\frac{132}{7}\text{ cm}^2}$
Final Answer: The area of the sector is $\mathbf{\frac{132}{7}\text{ cm}^2}$ (or $18.86\text{ cm}^2$).