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CBSE Areas Related to Circles Class 10th Formula

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Circumference or perimeter of a circle: The total length of boundary of a circle is called its circumference. Circumference of a circle = 2πr ; where ‘ r ’ is radius of the circle

• Area of circle : Area of circle of radius r = πr2

• Area of semicircle = ½ (Area of circle) = ½ πr2

• Area of quadrant = ¼ × Area of circle = πr2/4 

• Perimeter of Semicircle = ½ (Circumference of semicircle) + Diameter

= πr + 2r = (π + 2)r

 Area of a ring or Area enclosed between two concentric circles:

If ‘R’ is radius of outer circle and ‘r’ is radius of smaller (inner) circle. Then area enclosed between two concentric circles (or area of ring)

= πR2 - πr2

π(R2 - r2)

Length of arc, area of sector and segment: Let us consider an arc AB making an angle θ <180° at the centre of a circle of radius ‘r’. Then

(i) Length of arc ACB = 2πrθ/360°= l

(b) Area of major segment BDAB = (Area of the circle) – (Area of the minor segment ACBA) Rotating wheels:

<!--[if !supportLists]-->(i) Distance moved by a wheel in 1 rotation = Circumference of wheel

<!--[if !supportLists]-->(ii) Number of rotations in 1 minute = Distance moved in 1 minute/Circumference

• Rotations of the hands of a clock:

<!--[if !supportLists]-->(i) Angle described by the minute – hand of a clock in 60 minutes = 360°

<!--[if !supportLists]-->(ii) Angle described by the hour – hand of a clock in 12 hours = 360°

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