find the radian measure of the central angle of a circle of radius r = 6 meters that intercepts an arc of length s = 700 centimeters
To find the radian measure of the central angle, we need to use the formula:
s = rθ
where s is the length of the arc, r is the radius, and θ is the radian measure of the central angle.
Given that r = 6 meters and s = 700 centimeters, we need to convert the length of the arc from centimeters to meters. There are 100 centimeters in a meter, so:
s = 700 centimeters = 700/100 = 7 meters
Now we can substitute the values into the formula and solve for θ:
7 = 6θ
Dividing both sides by 6, we get:
θ = 7/6 ≈ 1.167 radians
Therefore, the radian measure of the central angle is approximately 1.167 radians.