## Area Related Circle Class 10 Formulas

Area Related Circle Class 10 Formulas PDF is Chapter 12 of Class 10 and you can download the Area Related Circle Class 10 Formulas PDF from the link given at the bottom of this page. Class 10th Students the concepts related to circles such as area, circumference, segment, sector, angle, and length of a circle, and area for the sector of a circle is provided here.

In the chapter “Areas related to circles” for Class 10, we will learn to find the areas of circles, areas of segments and sector of circles, circumference, length of the arc of a sector, etc. A circle is a two-dimensional figure. It is a curved-shape that has all its points at an equal distance from the center.

Parameters of Circles | Formulas |
---|---|

Area of the sector of angle θ | (θ/360°) × πr^{2} |

Length of an arc of a sector of angle θ | (θ/360°) × 2πr |

Area of major sector | πr^{2} – (θ/360°) × πr^{2} |

Area of a segment of a circle | Area of the corresponding sector – Area of the corresponding triangle |

Area of the major segment | πr^{2} – Area of segment (minor segment) |

**Area of Circle**

Area of a circle is πr^{2}, where π=22/7 or ≈ 3.14 (can be used interchangeably for problem-solving purposes) and r is the radius of the circle.

π is the ratio of the circumference of a circle to its diameter.

Example: Find the area of a circle with radius = 7cm.

Solution: Given, radius of circle = 7cm

By the formula we know;

Area of circle = πr^{2}

= π(7)^{2}

= (22/7) (7)^{2}

= 154 sq.cm.

**Circumference of a Circle**

The perimeter of a circle has a special name: Circumference, which is π times the diameter which is given by the formula;

Circumference of a circle = 2πr.

Example: The circumference of a circle whose radius is 21cm, is given by;

C = 2πr

= 2 (22/7) (21)

= 132 cm

**Area of a Sector of a Circle**

Area of a sector is given by

(θ/360°)×πr2

where ∠θ is the angle of this sector(minor sector in the following case) and r is its radius

**Length of an arc of a Sector**

The length of the arc of a sector can be found by using the expression for the circumference of a circle and the angle of the sector, using the following formula:

L= (θ/360°)×2πr

Where θ is the angle of sector and r is the radius of the circle.

**Area of a Triangle**

The Area of a triangle is,

Area=(1/2)×base×height

If the triangle is an equilateral then

Area=(√3/4)×a2 where “a” is the side length of the triangle.

**Area of a Segment of a Circle**

Area of segment APB (highlighted in yellow)

= (Area of sector OAPB) – (Area of triangle AOB)

=[(∅/360°)×πr2] – [(1/2)×AB×OM]

[To find the area of triangle AOB, use trigonometric ratios to find OM (height) and AB (base)]

Also, the Area of segment APB can be calculated directly if the angle of the sector is known using the following formula.

=[(θ/360°)×πr2] – [r2×sin θ/2 × cosθ/2]

Where θ is the angle of the sector and r is the radius of the circle.

**You can download the Area Related Circle Class 10 Formulas PDF using the link given below.**