Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev

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.
All you need of Class 10 at this link: Class 10

⇒ 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
⇒ Area of semicircle:
Area of semicircle =1/2 πr
Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
Area of a quadrant:
Area of a quadrant (quarter circle) = πr2/4
⇒ Perimeter of semicircle: 
Perimeter of a semicircle or protractor = πr+2r
Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
Area of the ring:
Area of the ring or an annulus
= πR2 - πr2 
= π(R2 - r2)
= π(R + r) (R - r)
Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
⇒ Length of arc AB = Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
⇒ Area of sector:
Area of sector OACBO = Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
or
Area of sector OACBO = 1/2(r x 1).
Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
⇒ Perimeter of sector: 
Perimeter of sector OACBO
= length of arc AB + 2r
Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
⇒ Area of segment: 
(i) Area of minor segment ACBA
= Area of sector OACBO - Area of ΔOAB = Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
(ii) Area of major segment BDAB
= Area of the circle - Area of minor segment ACBA
= πr2 - Area of minor segment ACBA.
⇒ If a chord subtend a right angle at the centre, then
Area of the corresponding segment = Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
⇒ If a chord subtend an angle of 60° at the centre, then
Area of the corresponding segment = Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
⇒ If a chord subtend an angle of 120° at the centre, then
Area of the corresponding segment = Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
⇒ Other important formulae:
(i) Distance moved by a wheel in 1 revolution = Circumference of the wheel
(ii) Number of revolutions in one minute = Important definitions and formulas - Areas Related to Circles Class 10 Notes | EduRev
(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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