Question

What is the radius of the circle whose diameter is 13 units?

Answer 1

Hint: We are given the diameter of the circle and we have to find the radius of this circle. Now, diameter is the distance between two points on a circle passing through the center. Hence, the diameter of the circle is 2 times its radius. Using this formula, we can find the radius of the given circle.

Complete step-by-step solution:
In this question, we are given a circle and its diameter. We have to find its radius.
$ \Rightarrow D = 13$units.
$ \Rightarrow r = $?
Now, first of all let us understand what circle, diameter and radius are.
So, a circle is the collection of all the points lying in a plane at a given distance from the center point.
The distance between the center and all the points on the circle is known as radius.
The distance between two points on the circle passing from the center is known as the diameter of the circle.

Now, the diameter is double in length as compared to the radius.
So, we can say that the diameter of the circle is equal to 2 times its radius.
 $ \Rightarrow d = 2r$
Now, we have the diameter as 13 units and we have to find the radius. Therefore,
$ \Rightarrow 2r = 13$
Divide both sides by 2, we get
$ \Rightarrow r = \dfrac{{13}}{2}$
$ \Rightarrow r = 6.5$ units
Hence, the radius of the circle having diameter 13 units is 6.5 units.

Note: To find the circumference of the circle, we can use the given two formulas.
When diameter is given:
$ \Rightarrow Circumference = \pi \times d$
For example: $d = 13$
$ \Rightarrow \text{Circumference} = 3.14 \times 13 = 40.82$
When radius is given:
$ \Rightarrow \text{Circumference} = 2 \times \pi \times r$
For example: $r = 6.5$
$ \Rightarrow \text{Circumference} = 2 \times 3.14 \times 6.5 = 40.82$