Pre-Requisires
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Areas Related To Circles | Speed Notes
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Introduction :
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. (Scroll down to continue …)
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AREAS AND PERI METER RELATED TO CIRCLES
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Introduction :
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 = d or 2r, where d is a diameter and r is a radius of the circle and = 227 or 3.14
Area of a circle:
Area of a circle = πr2
Area of a semicircle :
Area of semicircle = 12 πr2
Area of a quadrant :
Area of a quadrant (quarter circle) = r24
Perimeter of a semicircle:
Perimeter of a semicircle or protractor =πr+2r
Area of the ring :
Area of the ring or an annulus
= πR2 – πr2
= π(R2 – r2)
= π(R- r)(R+r)
Length of the arc AB
= 2πrθ3600 or πrθ1800
Area of a sector:
Area of sector OACBO =πrθ3600
OR
Area of sector OACBO = 12(r×l)
Perimeter of a sector :
Perimeter of sector OACBO
= Length of arc AB+2r
= πrθ1800+2r
Other important formulae :
(i) Distance moved by a wheel in 1 revolution = Circumference of the wheel.
(ii) Number of revolutions in one minute = Distance moved in 1 minuteCircumference
(iii) Angle described by minute hand in 60 minutes =3600
(iv) Angle described by hour hand in 12 hours = 3600
The midpoint 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.
Area of a segment:
(i) Area of minor segment ACBA
= Area of sector OACBO- Area of ∆OAB
= πrθ3600- 12r2sinθ
(ii) Area of major segment BDAB
= Area of the circle – Area of minor segment ACBA
=πr2 – Area of minor segment ACBA
If a chord subtends a right angle at the center, then
Area of the corresponding segment = 4-12r2
If a chord subtends an angle of 600 at the center, then
Area of the corresponding segment = 6-32r2
If a chord subtends an angle of 1200 at the center, then Area of the corresponding segment = 3-34r2
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