Points A and B lie on a circle centered at point O. If OA=5 and lenth of AB/circumference=1/4 what is the area of sector AOB? Us e the value pi =3.14
1 answer:
<h3>Given</h3>
arc AB of circle O is 1/4 of the circumference radius of circle O is 5 pi is 3.14 <h3>Find</h3>
<h3>Solution</h3>
Since arc AB is 1/4 of the circumference, the central angle AOB will be 1/4 of a circle, so π/2 in radians. The area of a sector is given by
... A = (1/2)r²·θ
where θ is the central angle in radians and r is the radus.
The area is ...
... A = (1/2)·5²·π/2 = 25π/4
... A ≈ 19.625
The area of the sector is about 19.63 square units.
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