# Area Of Sector And Segment Of A Circle

## Area Related To Circles of Class 10

**Length of arc, area of sector and segment**

Let an arc AB make an angle θ º < 180º at the centre of a circle of radius

Length of the arc =2πrθ/360

Perimeter of the sector OPRQO = OP + OQ + length of arc

Area of the minor segment PRQP = (area of the sector OPRQO ΔOPQ)

Area of the major segment QSPQ = (area of the circle) – (area of the minor segment PRQP)

**Q: If the following figure is a sector of circle of radius 10.5 cm. Find the perimeter of the sector.**

**Sol.** The arc length r = AB of a sector of an angle 60°in a circle of radius 10.5 cm is given by

Perimeter of sector

**Q: In the following figure, the length of an arc AB = 20πcm is a sector of a circle, find the radius of the circle.**

**Sol.**The arc of length AB= 20πcm of a sector of an angle 144° in a circle of radius ris given by

⇒cm.

**Q: What is the ratio of the area of sector of angle 30 in a circle and that of the complete circle?**

**Sol.**Area of a sector of angle 30°in a circle of radius r cm

∴

Thus the ratio is 1 : 12.

**Q: An arc of a circle is of length 5 cm and the sector is bounds has an area 20 π cm ^{2} . Find the radius of the circle.**

**Sol.** We know that Area of a sector bounded by a given arc = 1/2 x (length of a given arc) radius of a circle.

**Q: The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.**

**Sol.**Angle described by the minute hand in 60 minutes = 360º.

Angle described by the minute hand in 35 minutes ⇒θ= 210º and r = 12 cm.

⇒Area swept by the minute hand in 35 minutes

**Q: The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.**

**Sol.**Let O be the centre of a circle of radius 5.6 cm, and let OABO be its sector with perimeter 27.2 cm.

Then, OA + OB + arc AB = 27.2 cm.

⇒ 5.6 cm + 5.6 cm + arc AB = 27.2 cm.

⇒ arc AB= 16 cm.

Area of the sector OACBO

**Q: An umbrella has 8 ribs, which are equally spaced (figure). Assume umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.**

**Sol.**Here, r = 45º cm.

θ= sector angle between two consecutive ribs

360°/8= [ There are 8 sectors of same size] = 45º.

Therefore, the area between two consecutive ribs of the umbrella.

= The area of one sector.