Question

What is the length of an arc with a central angle of 4/3π radians and a radius of 42 centimeters?

Answer 1

First, we've got to convert radians to degrees.

blank degrees = 4π/3 * (180/π)
= 240

So, the arc we are measuring is 240 degrees.

Now let's find the length of the arc. 
The formula is θ/360 * 2πr

240/360 * 2 * (3.14) * 42

= 2/3 * 2 * 3.14 * 42

= 4/3 * 3.14 *42

= 12.56/3 *42

= 527.52/3

= 175. 84

The length of the arc is about 175.84 cm long.