Question

The angle of a sector of a circle of radius 4 cm is $60^\circ$. Its area will be

• A. $6\pi$ cm$^2$
• B. $8\pi$ cm$^2$
• C. $\dfrac{8}{3}\pi$ cm$^2$
• D. $3\pi$ cm$^2$

Hint:

For finding the area of a sector, always use the fraction of the total circle: $\dfrac{\theta}{360^\circ} \times \pi r^2$.

Answer 1

The Correct Option is C

Step 1: Formula for the area of a sector.
\[ \text{Area of a sector} = \dfrac{\theta}{360^\circ} \times \pi r^2 \] Step 2: Substitute the given values.
\[ r = 4 \text{ cm}, \, \theta = 60^\circ \] \[ \text{Area} = \dfrac{60}{360} \times \pi \times (4)^2 = \dfrac{1}{6} \times 16\pi = \dfrac{8}{3}\pi \, \text{cm}^2 \] Step 3: Conclusion.
Hence, the area of the sector is $\dfrac{8}{3}\pi$ cm$^2$.