Question

The area of the circular playground is$22176c{{m}^{2}}$. Find the cost of fencing this ground at the rate of Rs. 50 per metre.

Answer 1

Hint: First, by using the formula of the area A of the circle with radius r is given by$A=\pi {{r}^{2}}$. Then, by substituting the value of A as $22176c{{m}^{2}}$and then by calculating the value of r, we can proceed further. Then, we are supposed to find the length of the fence which is actually the circumference C of the circle by using the formula as $C=2\pi r$. Then, we need to find the cost of fencing the ground at the rate of 50 per metre by multiplying it with the rate of 50 per metre with circumference of circle.

Complete step by step answer:
In this question, we are supposed to find the cost of fencing this ground at the rate of Rs. 50 per metre when the area of the circular playground is$22176c{{m}^{2}}$.
So, before proceeding for this, we must know that the area of the field which is circular in the shape is $22176c{{m}^{2}}$and we must draw a circle with radius r as:

Then, by using the formula of the area A of the circle with radius r is given by:
$A=\pi {{r}^{2}}$
Now, by substituting the value of A as $22176c{{m}^{2}}$and then by calculating the value of r as:
$22176=\dfrac{22}{7}{{r}^{2}}$
Then, by solving the above expression to get the value of r as:
$\begin{align}
  & \dfrac{22176\times 7}{22}={{r}^{2}} \\
 & \Rightarrow 1008\times 7={{r}^{2}} \\
 & \Rightarrow {{r}^{2}}=7056 \\
 & \Rightarrow r=\sqrt{7056} \\
 & \Rightarrow r=84cm \\
\end{align}$
Then, we are supposed to find the length of the fence which is actually the circumference C of the circle.
So, we know the formula of the circumference C of the circle is:
$C=2\pi r$
The, by substituting the value of r as 84cm, we get:
$\begin{align}
  & C=2\times \dfrac{22}{7}\times 84 \\
 & \Rightarrow C=2\times 22\times 12 \\
 & \Rightarrow C=528cm \\
\end{align}$
So, we get the length of the fencing is 528cm.
Now, the length of fence in meters is 5.28m.
Now, we need to find the cost of fencing the ground at the rate of 50 per metre is given by:
$5.28\times 50=264$

Hence, we get the cost of fencing the circular playground as Rs. 264.

Note: Now, to solve these types of questions we need to know some of the basic conversions beforehand so that we can easily proceed in these types of questions. Then, some of the basic conversions are:
$\begin{align}
  & 1m=100cm \\
 & 1cm=\dfrac{1}{100}m \\
\end{align}$