SOLUTION: a sector of a circle has area 8.1pi cm squared and central angle 36 degrees. find its radius and arc length.

Algebra ->  Trigonometry-basics -> SOLUTION: a sector of a circle has area 8.1pi cm squared and central angle 36 degrees. find its radius and arc length.      Log On


   

Question 38934: a sector of a circle has area 8.1pi cm squared and central angle 36 degrees. find its radius and arc length.
Found 2 solutions by Earlsdon, fractalier:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If the sector has a central angle of 36 degrees, then its area is:%2836%2F360%29%28pi%29r%5E2, we can write:
%28pi%29r%5E2%2F10+=+8.1%28pi%29 Simplify and solve for the radius, r.
r%5E2+=+81
r+=+9cm.
The arc length will be 1%2F10 of the circumference or:
%281%2F10%292%28pi%29r Simplify.
2%289%29%28pi%29%2F10+=+%2818%2F10%29%28pi%29 = 1.8%28pi%29

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Well a sector of 36 degrees represents 1/10 of a circle...so the entire circle's area would be 81(pi)...setting that equal to the formula for area, we get
81(pi) = (pi)r^2
r^2 = 81
r = 9
Now the entire circumference is 2(pi)r = 18(pi), but we are talking about only 1/10 of a circle, thus the arc length is 1/10 of 18(pi), or 1.8(pi).