SOLUTION: Find the area of the sector formed by central angle θ = 3π/5 in a circle of radius r = 8 m. (Round the answer to two decimal places.)

Algebra ->  Trigonometry-basics -> SOLUTION: Find the area of the sector formed by central angle θ = 3π/5 in a circle of radius r = 8 m. (Round the answer to two decimal places.)       Log On


   

Question 412210: Find the area of the sector formed by central angle θ = 3π/5 in a circle of radius r = 8 m. (Round the answer to two decimal places.)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Central angles, their arcs and the areas of the sectors formed are all proportional:
     central angle           arc length           area of sector
  ------------------    =   -------------   =   ------------------
  2pi or 360 degrees        Circumference       area of the circle

For your problem, which references central angles and area of a sector, we will use the first and third fractions:
     central angle            area of sector
  ------------------    =   ------------------
  2pi or 360 degrees        area of the circle

Since your central angle is expressed in radians we will use 2pi in the denominator of the first fraction:
%283pi%2F5%29%2F2pi+=+x%2F%28pi%2A8%5E2%29
which simplifies to:
3%2F10+=+x%2F64pi
Cross multiplying we get:
192pi+=+10x
Dividing by 10 we get:
192pi%2F10+=+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.