All formulas for area related to circle class 10
Answers
Answer:
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 d is a diameter and r is a radius of the circle and π = 227
Area of a circle = πr2
Area of a semicircle = 12 πr2
Area of quadrant = 14 πr2
Perimeter of a semicircle:
Perimeter of a semicircle or protractor = πr + 2r
(refer semicircle image (1st image))
Area of the ring Formulas :
Area of the ring or an annulus = πR2 – πr2
= π(R2 – r2)
= π (R + r) (R – r)
Length of the arc AB = 2πrθ3600 = πrθ1800
(refer circle image (2nd image ))
Area of sector formula:
Area of sector OACBO = πr2θ3600
Area of sector OACBO = 12 (r × l).
Perimeter of a sector Formula:
Perimeter of sector OACBO = Length of arc AB + 2r
= πrθ1800 + 2r
(refer 3rd image )
Other important formulae:
Distance moved by a wheel in 1 revolution = Circumference of the wheel.
Number of revolutions in one minute = Distancemovedin1minuteCircumference
Angle described by minute hand in 60 minutes = 360°
Angle described by hour hand in 12 hours = 360°
The mid-point of the hypotenuse of a right triangle is equidistant from the vertices of the triangle.
The angle subtended at the circumference by a diameter is always a right angle.
Area of a segment Formula Class 10 :
(refer 4th image)
Area of minor segment ACBA = Area of sector OACBO – Area of ΔOAB
= πr2θ3600−12r2sinθ
Area of major segment BDAB = Area of the circle – Area of minor segment АСВА
= πr2 – Area of minor segment ACBA.
If a chord subtends a right angle at the centre, then
Area of the corresponding segment = (π4−12)r2
If a chord subtends an angle of 60° at the centre, then
Area of the corresponding segment = (π3−√32)r2
If a chord subtends an angle of 120° at the centre, then
Area of the corresponding segment = (π3−√34)r2
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