Question

How do you find the circumference of a circle whose area is $60\pi c{{m}^{2}}$?

Answer 1

Hint: For this problem we need to calculate the circumference of the circle with the given area. We know that the formula for area of the circle is $A=\pi {{r}^{2}}$ and the formula for the circumference of the circle is $C=2\pi r$. In both the formulas we can observe the common term which is $r$ radius of the circle. So, to calculate any parameter of the circle we need to have the value of the radius. So, from the given value of area, we will calculate the value of radius by using the formula for area of the circle. After having the value of the radius, we can calculate the circumference by substituting the value of radius in the formula.

Complete step by step answer:
Given that, the area of the circle is $60\pi c{{m}^{2}}$.
Let us assume the radius of the circle as $r$ cm.

We know that the area of the circle having the radius $r$ is $A=\pi {{r}^{2}}$. But in the problem, they have mentioned that the area of the circle as $60\pi c{{m}^{2}}$. So, equating the both the values, then we will have
$\pi {{r}^{2}}=60\pi $
Cancelling the term $\pi $ which is on both sides of the above equation, then we will get
$\Rightarrow {{r}^{2}}=60$
For calculating the value of $r$, we are going to apply square root on both sides of the above equation, then we will have
$\begin{align}
  & \Rightarrow \sqrt{{{r}^{2}}}=\sqrt{60} \\
 & \therefore r=2\sqrt{15} \\
\end{align}$
Now the circumference of the circle is given by
$\begin{align}
  & C=2\pi r \\
 & \Rightarrow C=2\pi \times 2\sqrt{15} \\
 & \Rightarrow C=4\pi \sqrt{15} \\
\end{align}$
After substituting the values $\pi =3.14$ and $\sqrt{15}=3.872$, we will get the value of circumference as
$\therefore C=48.66c{{m}^{2}}$

Note: In this problem we have the area of the circle in terms of $\pi $. So, we have calculated the value of radius easily. If you don’t have the area of the circle in terms of $\pi $, then we need to use the value of $\pi =\dfrac{22}{7}$ in the area of the circle formula and calculate the radius value.