NCERT Class X Chapter 11: Area Related To Circles

Question:

Radius, $ r = 6 $ cm
Angle of sector, $ \theta = 60^\circ $

Area of the sector

Area of a sector = $ \frac{\theta}{360^\circ} \times \pi r^2 $

Step 1: Write down the given values.

$$ r = 6 \text{ cm}, \quad \theta = 60^\circ $$

Step 2: Write the formula for the area of a sector.

$$ \text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2 $$

Step 3: Substitute the given values into the formula. Use $ \pi = \frac{22}{7} $.

$$ \text{Area} = \frac{60^\circ}{360^\circ} \times \frac{22}{7} \times (6)^2 $$

Step 4: Simplify the fraction $ \frac{60}{360} = \frac{1}{6} $ and calculate $ (6)^2 = 36 $.

$$ \text{Area} = \frac{1}{6} \times \frac{22}{7} \times 36 $$

Step 5: Multiply the numerators and denominators.

$$ \text{Area} = \frac{1 \times 22 \times 36}{6 \times 7} $$

Step 6: Calculate the value.

$$ \text{Area} = \frac{792}{42} = 18.857 \text{ cm}^2 $$

The area of the sector is $ 18.857 $ cm$^2$.