Question

Derive the formula of Area of segment ?

Class - 10th
Chapter - Area related to circles.

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Answer 1

Answer:

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Answer 2

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

Areas Related To Circles Notes CBSE Class 10 Maths

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

Areas Related To Circles Notes CBSE Class 10 Maths

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

Areas Related To Circles Notes CBSE Class 10 Maths

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.

Step-by-step explanation:

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