Find the area A of the sector of a radius 30 feet formed by the central angle radian.
A central angle is an angle whose vertex is at the center of a circle. The rays of a central angle subtend (intersect) an arc on the circle. The part of the circle between the rays of the angle and the arc subtended is called a sector. We have the following theorem.
Area of a sector
The area A of sector of a circle of radius r formed by a central angle of θ radians is
A = r2 θ
The value of r in the formula is 30 feet.
The value of θ in the formula is radian.
A (area) = *(30 feet)2 *
= 34.615 feet2