Question

Find the Expenditure of putting a barbed wire around a 4 hectare square field, if it costs Rs.45 per meter.

Answer 1

 Hint: Expenditure is the total amount of rupees invested/spent for the particular work to be done. Here, expenditure is calculated by finding the total length of the fence which is calculated by finding the total length of field on which the fencing needs to be done. In given question, the area of the square field is given so; we can determine the side by using the formula\[{\text{Area = }}{\left( {{\text{Side}}} \right)^2}\]. Using the sides of the field, determine the perimeter of the square field which is the total length of the outer fence of the field and multiply the result with the per meter cost to get the final cost of fencing barbed wire around the square field.

Complete step-by-step answer:
Area of square shaped farm \[{\text{ = 4 hectares}}\]
\[\left( {1{\text{ hectares = 10,000}}{{\text{m}}^{\text{2}}}} \right)\]
Hence, to get the area of the field in square meters, multiply 4 hectares with 10,000 square meters. Area of field in square meters is:
\[
  {\text{A = 4}} \times 1{\text{0,000}} \\
  {\text{ = 40,000}}{{\text{m}}^2} \\
 \]
Let the sides of the square field be $a$. Substitute $A = 40,000$ in the formula $A = {\left( a \right)^2}$ to determine the length of the side of the square.
$
  A = {\left( a \right)^2} \\
  {\left( a \right)^2} = 40,000 \\
 $
Taking square roots both sides-
$
  \sqrt {{{\left( a \right)}^2}} = \sqrt {40,000} \\
  a = \pm 200 \\
 $
As the sides cannot be negative so, the sides of the square field is $a = 200{\text{ m}}$
Since the given field is a square then, the perimeter will be the sum of all the sides of the field.
Substitute $a = 200{\text{ m}}$in the formula $P = 4a$ to determine the total length of the square field on which the barbed wire is to be fenced.
$
  P = 4 \times 200 \\
   = 800{\text{ m}} \\
 $
The cost of fencing by barbed wire is Rs.45 per meter .
Therefore, the total cost of fencing for $800{\text{ m}}$of barbed wire is the product of the total length of the field and cost of fencing per square meter.
\[
  {\text{C = 45}} \times {\text{800}} \\
  {\text{ = Rs}}{\text{.36,000}}{\text{.}} \\
 \]
Hence the total cost of fencing is \[{\text{Rs}}{\text{.36,000}}\]

Note: Since the cost of fencing is given per meter we need to find the total length to be fenced by barbed wire is found first.