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Question

In a circle of a radius 3 miles, the length of the arc that subtends a central angle of 4 radians is ? miles.

How many miles.

Answer 1

1 radian = 1 radius

4 radian = 4 radii

4 radian = 4 miles

Answer 2

Well the circumference is 2πr, and in once complete revolution there are 2π radians

So here you have (4/2π) revolutions, so number of miles is (4/2π) x 2πr miles = 4r miles = 12 miles

Mike