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

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) (Show Source): You can put this solution on YOUR website!
If the sector has a central angle of 36 degrees, then its area is:, we can write:
Simplify and solve for the radius, r.

cm.
The arc length will be of the circumference or:
Simplify.
=

Answer by fractalier(6550) (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).
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