Question

Areas Related to Circles (10 Periods)
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and
perimeter/circumference of the above said plane figures

Answer 1

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 = 22/7

Area of a circle = πr2

Area of a semicircle = 1/2 πr2

Area of quadrant = 1/4 πr2

★Perimeter of a semicircle:

Perimeter of a semicircle or protractor = πr + 2r

Area of sector formula:

Area of sector OACBO = πr2θ/3600

Area of sector OACBO = 1/2 (r × l).

★Perimeter of a sector Formula:

Perimeter of sector OACBO = Length of arc AB + 2r

= πrθ/180° + 2r

★Other important formulae:

Distance moved by a wheel in 1 revolution = Circumference of the wheel.

Number of revolutions in one minute = Distancemovedin1minute/Circumference

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.."