### Maths Class X Question Bank

Real Numbers
Polynomials
Arithmetic Progression
Triangles
Coordinate Geometry
Introduction to Trigonometry
Applications of Trigonometry
Circles
Construction
Areas related to Circles
Surface Area and Volumes
Statistics
Probability

# Formula Sheet – Area related to Circles – Class X

1. Perimeter (circumference) of a circle with diameter d (d = 2r, where r is the radius) is given by C = d = 2r
2. Perimeter of semicircle with radius
3. Area of a circle with radius is given by
4. Area of semicircle of radius
5. Area of a ring whose outer and inner radii are and respectively
6. If two circles touch internally then the distance between their centres is equal to the difference of their radii
7. The distance moved by a rotating wheel in one revolution is equal to the circumference of the wheel.
8. The number of revolutions completed by a rotating wheel in one minute
9. Length of an arc which substends an angle of at the centre
10. Sector of a circle is a region enclosed by an arc of a circle and its two bounding radii.

(i) Area of sector
(ii) Perimeter of sector

11. Minor sector : A sector of a circle is called a minor sector if the minor arc of the circle is a part of its boundary. In the above figure minor sector is OACB.

12. Major sector : A sector of a circle is called a major sector, if the major arc of the circle is a part of its boundary. In the above figure, OADB is the major sector.

13. The sum of the arcs of major and minor sectors of a circle is equal to the circumference of the circle.

14. The sum of the areas of major and minor sectors of a circle is equal to the area of the circle.

15. The area of a sector is given by where

16. Angle described by minute hand in minutes .
angle described by minute hand in one minute

Thus, the minute hand rotate through an angle of in one minute.

17. Angle described by hour hand in hours .

angle described by hour hand in 1 hour

Angle described by hour hand in one minute

Thus, hour hand rotates through in 1 minute.

18. A segment of a circle is the region bounded by an arc and a chord, including the arc and the chord.

19. Minor segment : If the boundary of a segment is a minor arc of a circle, then the corresponding segment is called a minor segment. In the figure, segment PQR (the are which is shaded) is a minor segment.

20. Major segment : A segment corresponding a major arc of a circle is known as the major segment. In the figure above segment PQSP is a major segment.

21. Area of minor segment PRQS

22. Area of major segment PSQ

– area of minor segment PRQ.

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