The document Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.

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**⇒ Circumference of a circle or Perimeter of a circle: **

The distance around the circle or the length of a circle is called its circumference or perimeter.

Circumference (perimeter) of a circle = πd or 2πr, where r is the radius of the circle and π=22/7 or 3.14.**⇒ Area of a circle:**

Area of a circle = πr^{2 }**⇒ Area of semicircle:**

Area of semicircle =1/2 πr^{2 }

⇒ **Area of a quadrant:**

Area of a quadrant (quarter circle) = πr^{2}/4**⇒ Perimeter of semicircle: **

Perimeter of a semicircle or protractor = πr+2r

⇒ **Area of the ring:**

Area of the ring or an annulus

= πR^{2} - πr^{2}

= π(R^{2} - r^{2})

= π(R + r) (R - r)

⇒ Length of arc AB = **⇒ Area of sector:**

Area of sector OACBO =

or

Area of sector OACBO = 1/2(r x 1).**⇒ Perimeter of sector:**

Perimeter of sector OACBO

= length of arc AB + 2r**⇒ Area of segment: **

(i) Area of minor segment ACBA

= Area of sector OACBO - Area of ΔOAB =

(ii) Area of major segment BDAB

= Area of the circle - Area of minor segment ACBA

= πr^{2} - Area of minor segment ACBA.

⇒ If a chord subtend a right angle at the centre, then

Area of the corresponding segment =

⇒ If a chord subtend an angle of 60° at the centre, then

Area of the corresponding segment =

⇒ If a chord subtend an angle of 120° at the centre, then

Area of the corresponding segment = **⇒ Other important formulae:**

(i) Distance moved by a wheel in 1 revolution = Circumference of the wheel

(ii) Number of revolutions in one minute =

(iii) Angle described by the minute hand in 60 minutes = 360°

(iv) Angle described by the hour hand in 12 hours = 360°

⇒ The mid-point of the hypotenuse of a right triangle is equidistant from the vertices of the triangle.

⇒ Angle subtended at the circumference by a diameter is always a right angle.

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