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- 1 Areas Related to Circles CBSE NCERT Notes Class 10 Maths Chapter 12 PDF

# Areas Related to Circles CBSE NCERT Notes Class 10 Maths Chapter 12 PDF

## Perimeter or Circumference of Circle

The circumference of a circle whose radius is r is C = 2πr.

### Class 10 Maths Chapter 12 Examples 1:

The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Given that r_{1} = 19 and r_{2} = 9.

Now, C = C_{1} + C_{2} ⇒ 2πr = 2πr_{1} + 2πr_{2} ⇒ r = r_{1} + r_{2} = 28 cm.

## Area of Circle

The area of a circle with radius r is A = πr^{2}.

### Class 10 Maths Chapter 12 Examples 2:

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Given that r_{1} = 8 and r_{2} = 6.

Now, A = A_{1} + A_{2} ⇒ πr^{2} = πr_{1}^{2 }+ πr_{2}^{2}

⇒ r^{2} = r_{1}^{2 }+ r_{2}^{2} ⇒ r^{2} = 64 + 36 = 100 ⇒ r = 10 cm

## Sector of Circle

The portion of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.

Shaded region OAPB is a sector of the circle with centre O and ∠ AOB is called the angle of the sector.

Unshaded region OAQB is also a sector of the circle.

From the figure below, OAPB is called the minor sector and OAQB is called the major sector

## Area of Sector of Circle

Area of sector of a circle with radius r is **πr ^{2}θ/360^{o}**.

### Class 10 Maths Chapter 12 Examples 3:

Find the area of the sector of a circle with radius 4 cm and of angle 30°.

Required area of sector of Circle = πr^{2}θ/360^{o} = 3.14 × 16 × 30/360 = 4.19 cm^{2}.

## Length of Arc of Sector of Circle

Length of an arc of sector of a circle with radius r is **2πrθ/360 ^{o}**.

### Class 10 Maths Chapter 12 Examples 4:

In a circle of radius 21 cm, an arc subtends an angle of 60° at the center. Find the length of the arc.

Length of an arc of sector of a circle with radius L = 2πrθ/360^{o }= 2 × 22/7 × 21 × 60 / 360 = 22 cm.

## Segment of Circle

The portion of the circular region enclosed between a chord and the corresponding arc is called a segment of the circle.

Shaded region APB is a segment of the circle with centre O.

Unshaded region AQB is also a segment of the circle.

From the figure below, APB is called the minor segment and AQB is called the major segment.

## Area of Segment of Circle

Area of the segment APB

= Area of the sector OAPB – Area of Δ OAB

= **πr ^{2}θ/360^{o}** –

**(r**

^{2}sinθ)/2### Class 10 Maths Chapter 12 Examples 5:

Find the area of the segment AYB as shown in figure below.

Area of the segment AYB

= Area of sector OAYB – Area of Δ OAB

= πr^{2}θ/360^{o} – (r^{2}sinθ)/2

= 22/7 × 21 × 21 × 120/360 – (21 × 21 × sin120)/2

= 462 – (441 × √3 / 2)/2

= 462 – 441√3/4

## Area of Combination of Plane Figures

In this, we need to find the area of shaded regions.

### Class 10 Maths Chapter 12 Examples 6:

Find the area of the shaded region in figure below, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

Using Pythagoras theorem, QR^{2} = PQ^{2} + RP^{2} = 576 + 49 = 625

⇒ QR = 25 ⇒ Radius of circle, r = QR/2 = 25/2

Shaded region = Area of Semi-Circle – Area of Right Angle Triangle

= πr^{2}/2 – 1/2 × 24 × 7

= 625π/2 – 91

Click below to get * CBSE Class 10 Maths Chapter wise Revision Notes PDF*.