Question

8
type the correct answer in each box. assume π = 3.14. round your answer(s) to the nearest tenth.
in this circle, the area of sector cod is 50.24 square units.
the radius of the circle is    units, and m \\(\overarc{ab}\\) is    units.

Explanation:

Step1: Find radius via sector area

The area of a sector is $\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2$, where $\theta=90^\circ$, $\text{Area}=50.24$, $\pi=3.14$.
$$50.24 = \frac{90^\circ}{360^\circ} \times 3.14 \times r^2$$
Simplify $\frac{90}{360}=\frac{1}{4}$:
$$50.24 = 0.785 \times r^2$$
$$r^2 = \frac{50.24}{0.785} = 64$$
$$r = \sqrt{64} = 8$$

Step2: Find arc length of $\overset{\frown}{AB}$

Arc length formula: $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta=30^\circ$, $r=8$.
$$L = \frac{30^\circ}{360^\circ} \times 2 \times 3.14 \times 8$$
Simplify $\frac{30}{360}=\frac{1}{12}$:
$$L = \frac{1}{12} \times 50.24 \approx 4.2$$

Answer:

The radius of the circle is 8 units, and $m\overset{\frown}{AB}$ is 4.2 units.