Question 945586
the arc length of a circle with a central angle of 70 degrees is equal to 70/360 * 2 * pi * r.


since the arc length is equal to 3 meters, the equation becomes:


3 = 70/360 * pi * r


solve for r to get r = (3 * 360) / (70 * 2 * pi).


that would make the radius equal to 2.455533408.


to see if this is correct, find the circumference of the circle with a radius of 2.455533408 and then find the length of an arc that has a central angle of 70 degrees.


the circumference of the circle is equal to 2 * pi * r which becomes equal to 2 * pi * 2.455533408 which is equal to 15.42857143.


the length of the arc is equal to 70 / 360 * 2 * pi * r.


since 2 * pi * r is equal to 15.42857143, then the equation becomes:


the length of the arc is equal to 70 / 360 * 15.42857143 which is equal to 3.


that confirms that the solution is correct and that the length of the radius is equal to 2.455533408.