Angle of Arc of circle

Question

The radius of a circle is 4 centimeters. What is the angle measure of an arc bounding a sector with area 6pi square centimeters

Answer 1

This is one of those situations where dealing with radians instead of degrees makes things simpler.

An angle in radians is defined by the ratio of the length of arc divided by the radius of the circle. θ = s / r. This also simplifies the formula for the area of a sector, A = 1/2 θ r². Combining these, we can substitute s / r for θ to say that A = 1/2 * s/r * r² which simplifies to A = 1/2 sr. Solving for s, we have 2A/r = s.

In our case, this is 2 * 6π / 4 = 3π.

Hope that helped!