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.