SOLUTION: The radius of circle O and the measure of central angle O are given. r=6; measure of angle O=30 a) Find the exact area of the sector determined by the central angle. b) Find

Algebra ->  Surface-area -> SOLUTION: The radius of circle O and the measure of central angle O are given. r=6; measure of angle O=30 a) Find the exact area of the sector determined by the central angle. b) Find      Log On


   



Question 180305: The radius of circle O and the measure of central angle O are given.
r=6; measure of angle O=30
a) Find the exact area of the sector determined by the central angle.
b) Find the exact length of the intercepted arc.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The radius of circle O and the measure of central angle O are given.
r=6; measure of angle O=30
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Assuming it's 30 degrees, that's 1/12 of the whole circle.
The area of the sector is 1/12 of the area of the circle, and the length of the arc is 1/12 of the circumference.
a) Find the exact area of the sector determined by the central angle.
A+=+pi%2Ar%5E2%2F12
A+=+36pi%2F12
Area =~ 9.425 square units
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b) Find the exact length of the intercepted arc.
Arc = 2pi*r/12
Arc = 12pi/12
Arc = pi units