Question 412210
Central angles, their arcs and the areas of the sectors formed are all proportional:
<pre>
     central angle           arc length           area of sector
  ------------------    =   -------------   =   ------------------
  2pi or 360 degrees        Circumference       area of the circle
</pre>
For your problem, which references central angles and area of a sector, we will use the first and third fractions:
<pre>
     central angle            area of sector
  ------------------    =   ------------------
  2pi or 360 degrees        area of the circle
</pre>
Since your central angle is expressed in radians we will use {{{2pi}}} in the denominator of the first fraction:
{{{(3pi/5)/2pi = x/(pi*8^2)}}}
which simplifies to:
{{{3/10 = x/64pi}}}
Cross multiplying we get:
{{{192pi = 10x}}}
Dividing by 10 we get:
{{{192pi/10 = x}}}
All that's left is to replace {{{pi}}} with a decimal (3.14159....), simplify the fraction and round off the answer. I'll leave that up to you.