Areas Related to Circles Class 10 Notes: Chapter 12

Areas Related to Circles Class 10 Notes i.e. for chapter 12 provided here are extremely useful for the class 10 students to prepare and revise this chapter in a more efficient way. The most important topics from this chapter include the following topics which are explained in detail below.

  • Area of a circle
  • Perimeter or circumference of a circle
  • Area of a sector of a circle
  • Area of a segment of a circle

Area and Circumference of a Circle

For a circle, its area can be calculated by measuring the region that is enclosed by its boundary. The perimeter of a circle or its circumference is defined as the length of the circle’s boundary. The formula for area and perimeter of a circle is given as-

Area of a Circle \(\pi r^{2}\)
Circumference of a Circle \(2\pi r\)

Area of a Sector of a Circle

A sector of a circle can be defined as the part of that particular circle which is in between any two chosen radii.

Area of a Sector of a Circle

In the above diagram, the shaded region is the sector of a triangle and its area and the length of an arc of a sector is given by-

\(Area\, of\, the\, sector\, of\, angle\, \theta\) \(\frac{\theta}{360}\times \pi\times r^{2}\)
\(Length\, of\, an\, arc\, of\, a\, sector\, of\, angle\, \theta\) \(\frac{\theta}{360}\times 2\pi r\)

Area of a Segment of a Circle

Consider the same figure as given above-

Area of a Segment of a Circle

In this, AB is a chord which divides the circle into two parts i.e. a major part and a minor part. Now, the Area of the segment APB can be found by-

Area of the segment APB = Area of the sector OAPB – Area of ∆ OAB

Or,

\(Area\, of\, the\, segment\, APB = \frac{\theta}{360}\times \pi r^{2} – area\, of\, triangle\, \bigtriangleup OAPB\)

Example Questions

Areas Related To Circles For Class 10
Areas Related To Circles For Class 10

Practice Questions

  1. Calculate the radius of a circle if its circumference is 528 cm.
  2. What is the area of the sector of angle 60 degrees if the radius of the circle is 10 cm?
  3. Find the area of the following figure: (Note: ABCD is a square of side 14 cm and APD and BPC are semicircles).

Practice Questions

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Practise This Question

Look at the following table below.
Class intervalClass mark0551010151520

Fill in  the blanks with the class marks of the corresponding class intervals.