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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
**

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

(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 r" /> then,Â Area enclosed by the two circles =
**

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,
**

Here, and

Hence, the length of the arc is

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

Now using Pythagoras theorem in , =

Let the height of the tunnel be

Area of = =

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

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.

Area of the minor segment

=

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

= =

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