A sector of a circle has a radius of 10 and an area of 20π. What is the arc length of the sector?
The radius of the circle = radius of the sector
Area of the circle is \(100\pi\)
Area of the sector = \(20\pi\)
The sector area is one-fifth of the area of the circle \((\frac{{100\pi}}{{20\pi}} = 5)\)
Therefore, by the well known ratios relating the areas, circumference and central angle of the full circle and a sector of the circle,
\(\frac{{Area of Sector}}{{Area of Circle}} = \frac{Arc Length of Sector}{Circumference of the Circle} = \frac{Central Angle of Sector}{Full Angle of Circle}\)
We can deduce that the Arc Length of the Sector will be one-fifth of the Circumference of the Circle.
Circumference of the Circle = \(2\pi*10 = 20\pi\)
Therefore, Arc Length of the Sector = \(\frac{{20\pi}}{{5}} = 4\pi\)
The Answer is C.
_________________