Questions: A sector of a circle of diameter 34 cm has a central angle of 168°. Find the arc length of the sector and the area of the sector. Round answers to 2 decimal places as needed. Arc length of sector ≈ cm Area of sector ≈ cm²

Solution Steps

Given the diameter of the circle \( d = 34 \, \text{cm} \), the radius \( r \) is calculated as: \[ r = \frac{d}{2} = \frac{34}{2} = 17 \, \text{cm} \]

Using the formula for the arc length \( L \) of a sector: \[ L = \frac{\theta}{360} \times 2\pi r \] where \( \theta = 168^\circ \) and \( r = 17 \, \text{cm} \), we substitute the values: \[ L = \frac{168}{360} \times 2\pi \times 17 \] Calculating this gives: \[ L \approx 49.85 \, \text{cm} \]

Using the formula for the area \( A \) of a sector: \[ A = \frac{\theta}{360} \times \pi r^2 \] we substitute the values: \[ A = \frac{168}{360} \times \pi \times (17)^2 \] Calculating this gives: \[ A \approx 423.7 \, \text{cm}^2 \]

Final Answer