Question

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? Use the value pi =3.14

Answer 1

Given

• arc AB of circle O is 1/4 of the circumference
• radius of circle O is 5
• pi is 3.14

Find

• area of sector AOB

Solution

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.