Question

What is the circumference of a circle with area $36\pi c{{m}^{2}}$?

Answer 1

Hint: For solving this question you should know about the relation of radius, circumference and diameter of a circle with one another or each other. And this relation is generally used for calculating the circumference or radius by each other. We know that the radius is half of the diameter or we can say that the diameter is double of a radius. And the circumference of a circle is equal to the product of diameter with $\pi $. And the area of a circle is $\pi {{r}^{2}}$.

Complete step-by-step solution:
In the question it is asked to determine the circumference of a circle when the area is given as $36\pi c{{m}^{2}}$. If we see in the diagram then,

We can see in this that the radius is denoted by $r$. Diameter is denoted as $d$ and the outer side of the circle is known as the circumference where the circle ends up. As we know that the radius is always half of a diameter for a circle and we can say that the diameter of a circle is double of the radius. It means $r=\dfrac{d}{2}$ or $d=2r$.
The circumference of a circle is the product of the angle of a circle that is $2\pi $ and radius $r$. So, the circumference of a circle is equal to $2\pi r$.
According to our question, we have to find the circumference of a circle., whose area is given as $36\pi c{{m}^{2}}$ . The area of a circle is $\pi {{r}^{2}}$, so,
$\begin{align}
  & \Rightarrow \pi {{r}^{2}}=36\pi c{{m}^{2}} \\
 & \Rightarrow {{r}^{2}}=36 \\
 & \Rightarrow r=6cm \\
\end{align}$
Now, the circumference of the circle of radius 6cm is given by the formula $2\pi r$,
$\Rightarrow 2\pi \times 6=12\pi cm$
So, the circumference of the circle is $12\pi cm$.

Note: During solving this type of questions you should be careful of taking values of radius. The maximum time question asks for the area of the circle or the circumference of the circle and gives the value of the diameter and we have to convert it into radius. And the area of the circle is the total area which is covered by the circumference till the centre of the circle.