Question

Point B is the center of the circle shown, and the length of arc AC is 8π. What is the area of the circle?

Answer 1

A

Explanation:

Answer 2

`A=324\pi \text{ units}^2\approx1017.88\text{ units}^2`

Explanation:

The formula for arc length is:

`\stackrel{\frown}{A}=2\pi r((\theta)/(360)})`

Where Θ is measured in degrees.

We know that the arc length is 8π when the degree is 80. So, substitute 8π for A and 80 for Θ:

`8\pi=2\pi r((80)/(360))`

Divide both sides by 2π:

`4=r(80)/(360)`

Simplify the fraction:

`4=(2)/(9)r`

Multiply both sides by 9/2:

`r=18`

So, the radius is 18.

Now, we can find the area of the circle. The formula for the area of a circle is:

`A=\pi r^2`

Substitute 18 into r:

`A=\pi (18)^2`

Simplify:

`A=324\pi \text{ units}^2\approx1017.88\text{ units}^2`

And we're done!