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Area is the space measured inside the boundary of the circle.

**Circle**

A locus of a point in a plane such that its distance from a fixed point in the plane is always the same is called a circle.

The fixed point is the centre and the fixed distance is called the** radius of the circle**.

A circle with centre O and the radius r is denoted by C(O, r)

Circumference is the perimeter of a circle.

### Area of Circle

The area of a circle is the area inside the circle enclosed by its circumference.

A locus of a point in a plane such that its distance from a fixed point in the plane is always the same is called a circle.

The fixed point is the centre and the fixed distance is called the

A circle with centre O and the radius r is denoted by C(O, r)

Circumference is the perimeter of a circle.

The area of a circle is the area inside the circle enclosed by its circumference.

r =$\frac{d}{2}$

Area is then calculated by multiplying $\pi$ and $r^{2}$

3. Given the circumference:

Circumference = 2 $\pi$ r

r = $\frac{circumference}{2 \pi}$ , r = $\frac{C}{2\pi}$

Area of the circle

If you are given the

Solid 3-dimensional figure of a circle is a sphere.

Given radius of the circle = 4 units

Area of the circle =$\pi \times (4)^{2}$

= (3.14) $\times$ 16 = 50.24 sq units.

Given the diameter of the circle,

Area of the circle = $\pi \times (14)^{2}$

= ($\frac{22}{7}$) $\times 14 \times 14$ (here $\pi$ = $\frac{22}{7}$)

= 22 $\times$ 2 $\times$ 14 = 616 sq units.

A diameter in a circle divides a circle into two equal arcs. The two arcs is called a semi circle. In simple words a semi-circle is a half circle.

Area of a semi circle is half the area of the given circle.

= $\frac{(\pi r^{2})}{2}$.

Diameter is the chord in circle passing through the centre of the circle. It is denoted by the letter ‘d’. It is the longest chord in a circle.

Given the diameter, the area of the circle can be calculated using the formula:

Area of the circle = $\frac{\pi d^{2}}{4}$ ($\pi$ = pi taken as 3.142 approx, d=diameter of the circle)

Given the diameter of a circle 8 units calculate the area of the circle.

Given, diameter = 8 units

Area of the circle = $\frac{\pi d^{2}}{4}$

= $\frac{(3.142)\times (8)^{2}}{4}$

= 50.272 sq units.

Sector of a circle:

If the arc is the minor arc then the sector formed is the minor sector. The remaining part of the circle is called the major sector of the circle.

The area inside this part is the area of the sector.

The angle at the centre of a circle is 360°, in other words ‘$2\pi$’ ($\pi$ = 180°)

Area of the circle is $\pi r^{2}$ , so the area of a sector with some angle ‘$\theta$’ less than $2\pi$ can be written as:

($\frac{\theta}{2\pi}) \times \pi r^{2}$

On further simplification, we get ($\frac{\theta}{2}) \times r^{2}$

Area of a sector

The segment containing the minor arc is called the minor segment and the segment containing the major arc is called the major segment. The centre of the circle lies in the major segment.

Area of a segment= $(\frac{r^{2}}{2}) \times (\theta - \sin \theta)$

(r= radius of the circle, $\theta$ is in radians)

Area of a segment = $(\frac{r^{2}}{2}) \times [(\theta \times \frac{\pi}{180}) - \sin \theta]$

(r= radius of the circle, $\theta$ is in degrees)