In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π/4 radians.
What is the arc length?
Use 3.14 for π .
To find the arc length, you need to use the formula:
Arc length = radius * central angle
Given that the radius is 6 m and the central angle is 7π/4 radians, you can substitute these values into the formula to calculate the arc length.
Arc length = 6 m * (7π/4 radians)
First, simplify the expression 7π/4 radians:
7π/4 radians = (7 * 3.14)/4 radians
= 21.98/4 radians
= 5.495 radians
Now, substitute the simplified value of the central angle into the arc length formula:
Arc length = 6 m * 5.495 radians
= 32.97 m (rounded to two decimal places)
Therefore, the arc length is approximately 32.97 meters.