# Areas Related to Circles - Class 10

Notes for areas related to circles chapter of class 10 Mathematics. Dronstudy provides free comprehensive chapterwise class 10 Mathematics notes with proper images & diagram.

**(1) For a circle of a radius , we have
**

**(i) Circumference =**

**(ii) Area =**

**(iii) Area of semi-circle =**

**(iv) Area of a quadrant =**

** For Example:Â **Find circumference and area of a circle of radius 4.2 cm

**Solution:Â**We know that the circumference and area of a Circle of radius given by, and respectively.

(i) Circumference of the circle

= =

(ii) Area of the circle

=

Hence, Circumference of the circle and area of the circle and area of the circle are Â and respectively.

(iii) Area of a semi-circle = = = = Â

(iv) Area of a quadrant = = Â

**(2) If R and r are the radii of two concentric circles such that then,Â Area enclosed by the two circles =
**

**The area enclosed between the concentric circle is 770 . If the radius of the outer circle is 21 , find the radius of the inner circle.**

*For Example:Â***Solution:Â**Let the radius of inner and outer radius be and respectively.

It is given that area that area enclosed between concentric circles is 770

Radius of the outer circle is 21

Then, area enclosed between the concentric circle

Hence, the radius of the inner circle is 14 cm.

**(3) If a sector of a circle of radius contains an angle of Then,
**

**(i) Length of the arc of the sector = Â = x(Circumference)**

**Find the Length of the arc of the sector that subtends an angle of at the centre of a circle of radius 4 cm.**

*For Example:Â***Solution:Â**The length of the arc is given by

Here, and

Hence, the length of the arc is

**(ii) Perimeter of the sector=
**

**The cross section of railway tunnel the radius of the circular part is 2m. if calculate the perimeter of the cross section.**

*For Example:Â***Solution:**We have

Now using Pythagoras theorem in , =

Let the height of the tunnel be

Area of = =

Perimeter of cross-section is = major arcÂ +Â =Â =Â

**(iii) Area of the sector= (Area of the circle)**

**AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm and divided the circle into two segments find the area of the minor segment**

*For Example:Â***Solution:**It is given that chord divides the circle into two segments

In

=

Let , then

In we have

=

Hence,

We know that the area of minor segment of angle in a circle of radius r is

Now, using the value of and we can find the area of minor segment

Hence, area of minor segment is

**(iv) Area of the segment = Area of the corresponding sector - Area of the corresponding triangle
**

**=**

** For Example:Â **The radius of a circle with centre O is 5 cm. two radii OA and OB are drawn at right angles to each other. Find the areas of segment made by chord AB.

**Solution:Â**Radius of the circle = 5 cm

Area of the minor segment

=

Area of minor segment = area of circle â€“ area of minor segment =

= =

Nyc

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