Question

In the figure, the area of sector OAB will be:

• A. 4 cm$^2$
• B. 4.19 cm$^2$
• C. 4.91 cm$^2$
• D. 5 cm$^2$

Hint:

The area of a sector is given by the formula $\frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle and $r$ is the radius.

Answer 1

The Correct Option is B

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 central angle and $r$ is the radius. For the sector OAB: - $r = 4$ cm - $\theta = 30^\circ$ Substituting these values into the formula: \[ \text{Area of sector} = \frac{30^\circ}{360^\circ} \times \pi \times (4)^2 \] \[ \text{Area of sector} = \frac{1}{12} \times \pi \times 16 \] \[ \text{Area of sector} = \frac{16\pi}{12} = \frac{4\pi}{3} \approx 4.19 \, \text{cm}^2 \]
Step 2: Conclusion.
Thus, the area of sector OAB is approximately 4.19 cm$^2$. The correct answer is (B).