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The radius of a circle is 8 meters. What is the angle measure of an arc bounding a sector with area 8л square meters?

The radius of a circle is 8 meters. What is the angle measure of an arc bounding a-example-1
User Foo
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Answer: 45 degrees.

Step-by-step explanation: We know that the area of a sector of a circle with radius $r$ and central angle $\theta$ is given by:

$$\text{Sector area} = \frac{\theta}{360^\circ} \pi r^2$$

Let $x$ be the angle measure of the arc we are looking for. Then the area of the corresponding sector is:

$$8\pi = \frac{x}{360^\circ} \pi (8)^2 = \frac{x}{360^\circ} \cdot 64\pi$$

Simplifying, we get:

$$\frac{x}{360^\circ} = \frac{8}{64} = \frac{1}{8}$$

Multiplying both sides by $360^\circ$, we get:

$$x = \frac{360^\circ}{8} = 45^\circ$$

Therefore, the angle measure of the arc bounding the sector with area 8π square meters is 45 degrees.

User Kennyhyun
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