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

What is the radius of the circle?

How to do I go about this?

Guest Mar 30, 2017

#1**+3 **

arc length = radius * angle measured in radians

Convert 80º to radians.

80º * (π / 180º) rad. = 4π / 9 rad.

24π = radius * 4π / 9

54 = radius

hectictar
Mar 30, 2017

#2**+3 **

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