A diameter is a section that connects two points that lie on thecircumference, that passes through the center of the circle. The diameter is actually twice the radius.

As in the case of the radius, as well as in the case of the diameter, there are an infinite number of diameters on the circumference, and all are identical in length.

Below is an example of a circle with several diameters marked in different colors.

Given the parts of the circle shown in the figure (white)

The diameter of the circle is $11\operatorname{cm}$

How much is the area of the shaded parts together?

The area of the shaded parts is the area of the circle minus the two sections, one of which extends by an angle of $30°$ and the other by an angle of $15°$

In the same way we can look at the parts like this:

In a circle, a cut is formed by an angle of $(120°)$ degrees.

Diameter of the angle $7\operatorname{cm}$

What is the dotted area?

Solution

The total circle has $360°$ degrees, $120°$ degrees is one third of $360°$ and therefore the area of the shape is equal to one third of the area of the circle.

We will use the formula for the area of the circle and replace accordingly.

Given the circle whose diameter $4\operatorname{cm}$

What is its area?

Solution

Diameter = Radius multiplied by $2$

That is to say

$2r=4$

Divide by $2$

$r=2$

Replace in the formula for the area of the circle $A=\pi r^2$

$A=\pi2^2=\pi\cdot4=4\pi$

Answer

$4\pi$

Review questions

What is the diameter of a circle?

The diameter of a circle is the straight line that passes through the center of the circle and touches from end to end of the circle, it is twice the radius.

Let's see the following image:

Do you think you will be able to solve it?

Question 1

In which of the circles is the center of the circle marked?