Area Related to Circles Class 10 Maths Formulas

The List of Important Formulas for Class 10 Areas Related to Circles is provided on this page. We have everything covered right from basic to advanced concepts in Areas Related to Circles. Make the most out of the Maths Formulas for Class 10 prepared by subject experts and take your preparation to the next level. Access the Formula Sheet of Areas Related to Circles Class 10 covering numerous concepts and use them to solve your Problems effortlessly.

Circumference of a circle = 2πr
Area of a circle = πr² …[where r is the radius of a circle]
Area of a semi-circle = \(\frac { { \pi r }^{ 2 } }{ 2 }\)
Area of a circular path or ring:

Let ‘R’ and ‘r’ he radii of two circles
Then area of shaded part = πR² – πr² = π(R² – r²) = π(R + r)(R – r)

Minor arc and Major Arc: An arc length is called a major arc if the arc length enclosed by the two radii is greater than a semi-circle.

If the arc subtends angle ‘θ’ at the centre, then the
Length of minor arc = \(\frac { \theta }{ 360 } \times 2\pi r=\frac { \theta }{ 180 } \times \pi r\)
Length of major arc = \(\left( \frac { 360-\theta }{ 360 } \right) \times 2\pi r\)

Sector of a Circle and its Area
A region of a circle is enclosed by any two radii and the arc intercepted between two radii is called the sector of a circle.
(i) A sector is called a minor sector if the minor arc of the circle is part of its boundary.
\(\hat { OAB }\) is minor sector.

Area of minor sector = \(\frac { \theta }{ 360 } \left( { \pi r }^{ 2 } \right)\)
Perimeter of minor sector = \(2r+\frac { \theta }{ 360 } \left( { 2\pi r } \right) \)

(ii) A sector is called a major sector if the major arc of the circle is part of its boundary.
\(\hat { OACB }\) is major sector
Area of major sector = \(\left( \frac { 360-\theta }{ 360 } \right) \left( { \pi r }^{ 2 } \right)\)
Perimeter of major sector = \(2r+\left( \frac { 360-\theta }{ 360 } \right) \left( { 2\pi r } \right)\)

Minor Segment: The region enclosed by an arc and a chord is called a segment of the circle. The region enclosed by the chord PQ & minor arc PRQ is called the minor segment.

Area of Minor segment = Area of the corresponding sector – Area of the corresponding triangle

Major Segment: The region enclosed by the chord PQ & major arc PSQ is called the major segment.
Area of major segment = Area of a circle – Area of the minor segment
Area of major sector + Area of triangle