Question

What is the difference between a radius and diameter?

Answer 1

Hint: A closed and round shaped figure is said to be a circle. It is a figure that is made up of infinitely many points, but it does not have any edge point or corners on it. It is a two dimensional figure containing both diameter and radius.

Complete step-by-step answer:
A circle is a two dimensional, closed curved figure that possesses a radius and diameter. Both radius and diameter have many applications in a circle and are very useful. They have similarities but they are very much different.
We can understand the differences between a radius of a circle and a circle’s diameter, more or less by observing the given figure.

Any circle can be denoted by its center. From the figure, the center of the circle is said to be $O$, so let us refer to the circle as;
Circle $O$
In this circle $O$, there are two different line segments that have been marked, where one among them is denoted as ‘$r$’ and the other line segment is denoted as ‘$d$’. By observation we can say that one is longer than the other.
We shall list out their differences:

Radius	Diameter
(i) While travelling around the circumference or path of the circle, the fixed length between the center and any point on the arc is said to form a radius.	(i) Any line that touches two points of the circumference is said to be a chord and the longest chord that passes through the center is termed as the diameter.
In given figure, the radii constructed are:$$\mathbf{OA},\mathbf{OB},\mathbf{OC}$$	In the given figure, the only diameter constructed is:$$\mathbf{AB}$$
(ii) In Mathematical terms we can write the expression of a radius as: $$\mathbf{r}$$So the radius is always a constant.	(ii) The expression of diameter is: $$\mathbf{d}=\mathbf{2}\mathbf{r}$$Diameter is always twice the length of the fixed radius.
(iii) In terms of radius the area of a circle becomes:$\pi r^2$ where $r$ is the radius.	(iii) Using the diameter we can find the area of the circle like this:$\pi ({\displaystyle \frac{d}{2}}{)}^2$, where $d=2r$ is the diameter.
(iv) Any two radii along with an arc (smaller) of the circle are able to enclose an area which is commonly called as a sector.	(iv) A chord drawn by joining two points on the circle; encloses an area with the arc which is called a segment. This can be made by a diameter since it is a chord.
Example: If a circle has a radius of $3$, the diameter of the circle becomes $2\times 3=6$.	Example: If a circle has a diameter $6$, then the circle’s radius will be ${\displaystyle \frac{6}{2}}=3$.

Note: A similarity between the radius and diameter of a circle are that they are both constructed with respect to the center of the circle. When a line is constructed from the center to any point on a circle, it becomes a radius; while diameter is constructed by tracing a line from a point on an arc of the circle to the circle’s center then continuing from the center to another point on the opposite arc of the circle.