Question

How can I find the diameter of a circle?

Answer 1

Hint: There are different ways to find the diameter of a circle. In case we are given the radius of the circle then the diameter is double the radius of the circle. There can be other cases also, in case we are given the perimeter of a circle then we can easily calculate the diameter of a circle by dividing the given perimeter by $\pi $. There can be other answers also.

Complete step by step solution:
Finding the diameter(D) of a circle, when

Case 1: Radius of the circle is given. We know that the radius of the circle is half of the diameter of a circle. So we will get diameter value by doubling the radius.
$\text{Radius} (r)=\dfrac{\text{Diameter (D)} }{2}$
$\Rightarrow D=2r$ -(1)

Case 2: Perimeter of the circle is given. We will divide the perimeter by $\pi $.
$\text{Perimeter}=2\pi r$
From equation (1), we know that $D=2r$, so dividing the above equation by $\pi$, we get the diameter.
$D=\dfrac{\text{Perimeter}}{\pi}=\dfrac{2 \pi r}{\pi}$

Case 3: Area of the circle is given, we will calculate the diameter by first finding the radius by the formula
$A = \pi {r^2}$ and then doubling the radius. In case we are given a circle and then we have to find its diameter we will first take two points on a circle and then construct a perpendicular bisector through it that bisector will pass through the centre. Then the part of the perpendicular bisector after extending it end to end from the circle we will get the diameter. This way we can easily find the diameter of a circle.

Note:
The formula for the area of a circle is given by:
$A = \pi {r^2}$
And the formula for the perimeter of the circle is given by:
$A = 2\pi r$.
We can remember these formulas for making simpler calculations. Even if you don’t remember the formula, it won’t be a great concern. Just remember the Logic that the diameter of the circle is as twice as the radius of the circle. or Remember Diameter of the circle as a straight line that goes one side to the opposite and right through the centre of the circle.