The length of minor arc $AB$ of circle with area $\displaystyle 81\pi $ square units and $\angle ACB = $ $\displaystyle { 120 }^{ \circ }$ is

The area of the circle is given by the formula pi times the radius squared, so pi times r squared equals 81 pi, making the radius 9 units. The central angle for the minor arc AB is 360 degrees minus the given inscribed angle of 120 degrees multiplied by 2, which yields 120 degrees. Using the arc length formula, arc equals central angle divided by 360 times 2 times pi times r, we get 120 divided by 360 times 2 times pi times 9, resulting in 6 pi.

• Thanks
• Wrong explanation