The relation between arc of the circle, angle subtended by the arc at the centre and radius is

The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc. For example, in the circle shown below, O P is the arc of the circle with center Q . The arc length of this arc O P is given as L . The arc length formula in radians can be expressed as, arc length = θ × r , when θ is in radian. Arc Length = θ × π 180 × r , where θ is in degree, where, L = Length of an Arc θ = Central angle of Arc r = Radius of the circle

Find the length of arc and area of sector of the circle, if the angle subtended at the centre and the radius are 60 ° and 6 cm respectively.

Given radius of circle r = 6 cm , Angle subtended at the centre of the circle θ = 60 ° We know that, Length of an arc = θ 360 ° × 2 π r = 60 ° 360 ° × 2 π × 6 = 1 6 × 2 π × 6 = 2 π cm Area of the sector of the circle = θ 360 ° × π r 2 = 60 ° 360 ° × π × 6 2 = 1 6 × π × 6 2 = 6 π cm 2

In a circle of radius 21 cm an arc subtends an angle of 60 ° at the centre. Find the area of the sector.

Given radius r of circle = 21 c m And angle subtended by given arc = 60 o We know that, area of sector of angle θ , A = θ 360 o × π r 2 ⇒ Area of sector O A C B = 60 o 360 o × π r 2 = 1 6 × 22 7 × 21 × 21 = 231 c m 2