High School

Points A and B lie on a circle centered at point O. If \( OA = 5 \) and \( \angle AOB \) is given, what is the area of sector AOB? Use the value \(\pi = 3.14\), and choose the closest answer.

A. 19.6 square units
B. 39.3 square units
C. 7.85 square units
D. 15.7 square units

Answer :

The area of sector AOB whose radius OA 5 units is 19.6 sq. units.

What is the Sector?

A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.

Here, Radius of Circle = 5 units

length of arc AB / circumference = 1/4

So, Area of Sector AOB = one fourth of area of circle

= 1/4 X π X r²

= 0.25 X 3.14 X 5²

= 0.25 X 3.14 X 25

= 19.625 sq. units

Thus, the area of sector AOB whose radius OA 5 units is 19.6 sq. units.

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