Question

A sector of a circle having a radius of 10 cm and has a central angle of ⅚ radians. What is the area of the sector?

• A. 26.18 cm²
• B. 8.33 cm²
• C. 10.47 cm²
• D. 12.5 cm²

Answer 1

Answer:

A. 26.18 cm²

For a sector with radius (r) and central angle (\theta) in radians:

$\text{Area of sector}=\frac{1}{2}r^2\theta$

Substitute (r=10) cm and $(\theta=\frac{\pi}{6}):$

$\text{Area}$
$=\frac{1}{2}(10)^2\left(\frac{\pi}{6}\right)$

$=\frac{100\pi}{12}$

$=\frac{25\pi}{3}$

$\text{Area} \approx \frac{25 \times 3.1416}{3}$

$\approx 26.18 \text{ cm}^2$

Answer:$(\frac{25\pi}{3}\ \text{cm}^2 \approx 26.18\ \text{cm}^2).$