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# Can someone help me with this?

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A circle has an arc of length 24π that is intercepted by a central angle of 80°.

What is the radius of the circle?

Guest Mar 30, 2017
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24π = radius * 4π / 9

hectictar  Mar 30, 2017
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A circle has an arc of length 24π that is intercepted by a central angle of 80°.

What is the radius of the circle?

The circumference of a circle is $$2\pi r$$

You have

$$\frac{80}{360} \text{ of the circle}\\ so\\ \frac{80}{360}*2\pi r = 24\pi\\ \frac{8}{36}*2 r = 24\\ \frac{4}{9}* r = 24\\ r = 24*\frac{9}{4}\\ r =54\;units$$

check

80/360*2*pi*54 = 75.3982236861550377

24*pi = 75.3982236861550377

Melody  Mar 30, 2017