Question

An arc of a circle of radius 6 cm subtends an angle of \( 60^\circ \) at the centre. The area of the sector will be:

• A. \( 2 \pi \, \text{cm}^2 \)
• B. \( 4 \pi \, \text{cm}^2 \)
• C. \( 6 \pi \, \text{cm}^2 \)
• D. \( 8 \pi \, \text{cm}^2 \)

Hint:

The area of a sector is calculated by the formula \( \frac{\theta}{360^\circ} \times \pi r^2 \), where \( \theta \) is the angle subtended and \( r \) is the radius.

Answer 1

The Correct Option is A

The area of a sector is given by the formula: \[ \text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2 \] where \( \theta \) is the angle subtended at the centre and \( r \) is the radius. Here, \( \theta = 60^\circ \) and \( r = 6 \) cm. Substituting the values: \[ \text{Area of Sector} = \frac{60^\circ}{360^\circ} \times \pi \times 6^2 = \frac{1}{6} \times \pi \times 36 = 6 \pi \, \text{cm}^2 \] Thus, the area of the sector is \( 6 \pi \, \text{cm}^2 \).