CBSE Areas Related to Circles Class 10th Formula
Answers:
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°