Area Related to Circles - Revision Notes

 CBSE Class 10 Mathematics

Revision Notes
CHAPTER 12
AREAS RELATED TO CIRCLES

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1. Perimeter and Area of a Circle
2. Areas of Sector and Segment of a Circle
3. Areas of Combinations of Plane Figures
4. Miscellaneous Questions

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• Perimeter or Circumference of the circle = 2πr,$2\pi r,$ where r$r$ is the radius of the circle.

          Or Circumference of the circle = πd,$\pi d,$ where d$d$ is the diameter of the circle.

• Area of circle = πr2$\pi r^2$ where ‘r’ is the radius of the circle.
• Area of Semi circle = πr22$\frac{\pi r^2}{2}$
• Area enclosed by two concentric circles
  = π(R2−r2)$\pi (R^2-r^2)$
  = π(R+r)(R−r);      R>r$\pi (R+r)(R-r);R>r$

 

where ‘R’ and ‘r’ are radii of two concentric circles.

• The arc length ‘l$l$’ of a sector of angle ′θ′${}^{\prime }{\theta }^{\prime }$ in a circle of radius ‘r’ is given by

l=θ360o×2πr$l=\frac{\theta }{{360}^o}\times 2\pi r$

l=θ180o×πr$l=\frac{\theta }{{180}^o}\times \pi r$

• If the arc subtends an angle θ$\theta$, then area ofthe corresponding sector is θ360o×πr2$\frac{\theta }{{360}^o}\times \pi r^2$

The sector which is less than the semicircular region, is called the minor sector and the sector, which is more than the semicircular region is called the major sector.

• Area of segment= Area of sector - Area of corresponding triangle
• Area of major segment = Area of circle - Area of minor segment
• Angle described by minute hand in 60 minutes = 360°. Angle described byminute hand in 1 minute =(360o60)=6o