Question

The area of a circular field is 11.45 hectares, find the cost of fencing it at the rate of Rs 1.20 per meter.
A.Rs 1450
B.Rs 1433.136
C.Rs 1466.45
D.Rs 1540.33

Answer 1

Hint: 1 hectares is equal to 10000 m and fencing means getting boundaries over the farm. So here we need to find the length of the boundary and later the cost for that particular length for fencing it which is Rs 1.20 per metre.

Complete step-by-step answer:
Let’s begin with the given information where the area of the farm i.e., circular farm is 11.45 hectares which is
11.45 $\times $ 10000 m$^{2}$ = 114500 m$^{2}$
By using the formula of a square we can find a radius, which eventually helps to find the circumference. Circumference is required to know the total cost. So let’s proceed with the basic circular formula,
\[\begin{align}
  & \text{area}\,\text{=}\,\text{114500}\,\text{=}\,\text{ }\!\!\pi\!\!\text{ }{{\text{r}}^{\text{2}}} \\
 & {{\text{r}}^{\text{2}}}\,\text{=}\,\dfrac{\text{114500}}{\text{ }\!\!\pi\!\!\text{ }}\,\text{=}\,\dfrac{\text{114500}\,\text{ }\!\!\times\!\!\text{ }\,\text{7}}{\text{22}}\,\text{=}\,\text{3643}\text{.18182} \\
 & \text{r}\,\text{=}\,\text{190}
\end{align}\]
Let’s take out the circumference,
$\text{2 }\!\!\pi\!\!\text{ r}\,\text{=}\,\text{2}\,\text{ }\!\!\times\!\!\text{ }\,\dfrac{\text{22}}{\text{7}}\,\text{ }\!\!\times\!\!\text{ 190}\,\text{=}\,\text{1194}\text{.28}\,\text{m}$
For 1m amount required is Rs 1.2
Therefore, for 1194.28 m. the amount required will be
Rs 1194.28 x 1.2
= Rs 1433.136
Hence, the total cost for fencing will be Rs 1433.136
Option B is the correct answer

Note: Take Appropriate value of π according to the conditions which is 3.14 as well 22/7. Try to take the nearest whole number during the square root of a long number. It will help out further in multiplication for cost finding or length or area.