Term	Definition
area	The size of a two-dimensional surface.
arc	A portion of the circumference of a circle.
annulus	A ring-shaped object.
chord	A straight line segment whose endpoints both lie on the circle.
circumference	The distance around the circle. It is the circle's perimeter.
centre	The point inside a circle that is the same distance from each point on the circle.
diameter	Straight line segment that passes through the centre of the circle and whose endpoints lie on the circle.
radius	The distance from the centre of a circle or a sphere to any point on the circle or a sphere.
ratio	A comparison of two numbers by division.
sector	A pie-shaped part of a circle.
segment	The part of a line that connects two points.

Learn Now >>

😃CIRCLES💓

HOW TO FIND CIRCUMFERENCES OF A CIRCLE ?😊

HOW TO FIND AREA OF CIRCLE?😉

PARTS OF CIRCLE😉

ARC OF A CIRCLES😮

AREA OF A SECTOR OF A CIRCLES😙

Learn Now >>

Area of Sector of a Circle 😊

The formula is given below.

      2. Sector of a circles.

                   A part of the interior of a circle bounded by two radii and an arc.

      3. Properties .

                

Radius		The radius of the circle of which the sector is a part
Central    Angle		The angle subtended by the sector to the center of the circle.
Arc length		The length around the curved arc that defines the sector (shown in                              red here). Proceed to do Quiz

Learn Now >>

Area of a circles😇

The distance around a circle is called its circumference. The distance across a circle through its center is called its diameter. We use the Greek letter (pronounced Pi) to represent the ratio of the circumference of a circle to the diameter. In the last lesson, we learned that the formula for circumference of a circle is: . For simplicity, we use = 3.14. We know from the last lesson that the diameter of a circle is twice as long as the radius. This relationship is expressed in the following formula: .



                                                                 

The formula of area of a circles is :

                                            



Example questions to find area of a circle :

Question 1

Question 2

                                                    

Question 3

                                            

 Move to next topic  ➡  Area of Sector of a Circle 

Learn Now >>

ARC OF A CIRCLES 😎

An arc is a portion of the total circumference of a circle. The arc of a circle is denoted by the symbol "⌢$⌢$".


           

Arc of a Circle Equation

              

In the figure, PQ is an arc of the circle with the same degree measure as central angle POQ. The shorter distance between P and Q (drawn in red) and longer distance between P and Q (drawn in blue) along the circle is called the minor arc and major arc respectively.

Arc Length of a Circle

In the above figure, the part of the circle L is called the arc of the circle.

Arc Length of a Circle Formula

The length of an arc of a circle with radius r and subtending an angle θ$\theta$ in the center of the circle is defined as,

• If θ$\theta$ is in radians, L = θ$\theta$ * r
• If θ$\theta$ is in degrees, L = θ360o$\frac{\theta }{{360}^o}$ * 2 π$\pi$ r

This is the formula for finding length of the arc of a circle. This is based on the principle that the total angle at the centre is 360 degrees. So, the arc subtending an angle θ$\theta$ will be θ360o$\frac{\theta }{{360}^o}$ * 2 π$\pi$ r. This can be used to find the length of the arc of a circle. The length of the arc to the perimeter is in the same proportion as the subtended angle to the centre to 2π$\pi$ radians.

For an arc with a central angle measuring θ$\theta$ degrees:

Arc Length = θ360$\frac{\theta }{360}$ * (Circumference of circle)

Where Circumference = 2π$\pi$ r (r = radius of a circle).

Area of Arc of Circle

To determine the area of a sector bounded by 2 radii and an arc in the circle, use the same method used to find the length of an arc.

                                                   

In a sector whose central angle measures is θ$\theta$ degrees.

Area of sector = θ360$\frac{\theta }{360}$ * Area of circle

Where, Area of circle = π$\pi$ r2$r^2$ (r = radius of a circle).

Let us find the area of the sector of the circle with 60 at the centre and radius 7.

Area of the sector = 60360$\frac{60}{360}$ * (227$\frac{22}{7}$ * 7 * 7) 

= 1546$\frac{154}{6}$

= 773$\frac{77}{3}$.

Move to next topic ➡ Area of a Circle

Learn Now >>