Question

The radius of a circular garden is \[56m\]. What would it cost to put a \[4\] round fence around this garden at a rate of \[40\] rupees per meter.

Answer 1

Hint: We solve this question by first finding the perimeter of the circular garden by the formula, \[P = 2\pi r\] where, P is the perimeter of the circular garden and r is the radius of the circular garden. We should keep in mind that fencing is done only on the borders, so we find a perimeter. Now, we multiply this perimeter by 4 as we are putting a \[4\] round fence, then we will find the total cost.

Complete step-by-step answer:
We are given a circular garden with radius \[56m\] , so here \[r = 56m\].
Now, we will find the perimeter of the field which is to be fenced as fencing is done only on the borders,
So,
\[P = 2\pi r\]
Substituting the values, we get,
\[P = 2 \times \dfrac{{22}}{7} \times 56\]
Cancelling common factors in numerator and denominator, we get,
\[P = 2 \times 22 \times 8\]
Simplifying the calculations,
\[P = 352m\]
Therefore, perimeter of this circular garden is \[352m\]
Now, we will find a perimeter of 4 such gardens as we are putting a \[4\] round fence.
So, perimeter of 4 such rounds is
\[4P = 4 \times 352 = 1408m\]
Cost of fencing of \[1m\] is Rs \[40\].
So, the cost of fencing of \[1408m\] is Rs \[1408 \times 40 = 56320\].
So, the cost of fencing of \[1408m\] is \[56320\] rupees.
So, the correct answer is “Rs 56320”.

Note: Perimeter of circle is also known as circumference of circle which is given by formula, \[P = 2\pi r\] where, P is the perimeter of a circular garden and r is the radius of the circular garden. Also, keep in mind that fencing is done only on the borders of gardens, so we find perimeter first, as perimeter is the length of boundary. Take care while doing the calculations.