If $$B$$ is the center of the circle in the figure above and the area of the shaded region is $$16 \pi$$, what is the length of arc $$ADC$$?

Next use this to find the circle's radius:
> $$\pi r^2=64 \pi$$
> $$r^2=64$$
> $$r=8$$

Now, find the circle's circumference:

> $$\text{Circumference} = 2\pi r = 2\pi(8) =16 \pi$$ Since Arc $$ADC$$ is one-fourth of the circumference, >$$\text{Arc } ADC = \frac{1}{4} \times 16 \pi = 4 \pi$$.Incorrect.

[[snippet]]Incorrect.

[[snippet]]This is the value of the circle's circumference:

$$2 \pi r = 2\times8\times \pi = 16 \pi$$Now, you have one more step . . .

Incorrect.

[[snippet]]Incorrect.

[[snippet]]Correct.
[[snippet]]
When you plug in the given information, you get
> $$\displaystyle{\frac{16 \pi}{\text{Circle Area}}=\frac{90^\circ}{360^\circ}}$$
> $$\displaystyle{\frac{16 \pi}{\text{Circle Area}}=\frac{1}{4}}$$
Therefore,
> $$\text{Circle Area} = 4\times16 \pi = 64 \pi$$

$$4$$

$$4 \pi$$

$$16$$

$$8 \pi$$

$$16 \pi$$

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