Important Definitions & Formulas: Areas Related to Circles

# Important Definitions & Formulas: Areas Related to Circles | Mathematics (Maths) Class 10 PDF Download

⇒ 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 r is the radius of the circle and π=22/7 or 3.14.
⇒ Area of a circle:
Area of a circle = πr
⇒ Area of semicircle:
Area of semicircle =1/2 πr

Area of a quadrant (quarter circle) = πr2/4
⇒ Perimeter of 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 arc AB =

⇒ Area of sector:
Area of sector OACBO =
or
Area of sector OACBO = 1/2(r x 1).

⇒ Perimeter of sector:
Perimeter of sector OACBO
= length of arc AB + 2r

⇒ Area of segment:
(i) Area of minor segment ACBA
= Area of sector OACBO - Area of ΔOAB =

(ii) Area of major segment BDAB
= Area of the circle - Area of minor segment ACBA
= πr2 - Area of minor segment ACBA.
⇒ If a chord subtend a right angle at the centre, then
Area of the corresponding segment =
⇒ If a chord subtend an angle of 60° at the centre, then
Area of the corresponding segment =
⇒ If a chord subtend an angle of 120° at the centre, then
Area of the corresponding segment =
⇒ Other important formulae:
(i) Distance moved by a wheel in 1 revolution = Circumference of the wheel
(ii) Number of revolutions in one minute =
(iii) Angle described by the minute hand in 60 minutes = 360°
(iv) Angle described by the hour hand in 12 hours = 360°
⇒ The mid-point 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.

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## Mathematics (Maths) Class 10

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## FAQs on Important Definitions & Formulas: Areas Related to Circles - Mathematics (Maths) Class 10

 1. What is the formula to find the area of a circle?
Ans. The formula to find the area of a circle is A = πr², where A represents the area and r represents the radius of the circle.
 2. How do you find the circumference of a circle?
Ans. The circumference of a circle can be found using the formula C = 2πr, where C represents the circumference and r represents the radius of the circle.
 3. What is the difference between diameter and radius?
Ans. The diameter of a circle is a straight line passing through the center of the circle and it is equal to twice the radius. The radius of a circle is the distance from the center to any point on the circle.
 4. How do you find the area of a sector?
Ans. To find the area of a sector, you can use the formula A = (θ/360) × πr², where A represents the area, θ represents the central angle of the sector, and r represents the radius of the circle.
 5. How do you find the length of an arc?
Ans. The length of an arc can be found using the formula L = (θ/360) × 2πr, where L represents the length of the arc, θ represents the central angle of the arc, and r represents the radius of the circle.

## Mathematics (Maths) Class 10

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