     Question Answers

# The cost of fencing a circular field at the rate Rs. 24 per metre is Rs. 5280. The field is to be ploughed at the rate of Rs.0.50 per ${m}^2$. Find the cost of ploughing the field. (Take $\pi = \dfrac{{22}}{7}$) (A) Rs. 1278 (B) Rs 1437(C) Rs 1925(D) Rs 2870  Hint: First find the circumference of the circular field by using the given data. Later find the radius ‘r’ from the circumference formula $2 \pi r$, using this radius find the area of a circular field. To find the cost of ploughing the field multiply the area with the rate of ploughing the field.

Given: Total cost of fencing the circular field = Rs. 5280

Rate of fencing the circular field = Rs. 24/m

Rate of ploughing the circular field = Rs. $0.5/m^2$

Since, we know that fencing occurs around the circumference and ploughing is done on the area of the circular field.

Therefore, Circumference of the circular field = $\dfrac{{{\text{Total cost of fencing the circular field}}}}{{{\text{Rate of fencing the circular field }}}}$

If 'r' is the radius of the circular field, then its circumference is $2 \pi r$ where $\pi = \dfrac{{22}}{7}$

$\Rightarrow$ Circumference=$\dfrac{{5280}}{{24}}=2 \pi r$

$\Rightarrow r = \dfrac{{5280}}{{24 \times 2\pi }} = \dfrac{{5280 \times 7}}{{24 \times 2 \times 22}} = 35{\text{ }}m$

So, the radius of the circular field is 35 metres.

Area of the circular field = $\pi {{\text{r}}^2} = \dfrac{{22}}{7} \times {35^2} = 3850{\text{ }}{m^2}$

Now, Total cost of ploughing = (Area of the circular field)$\times$(Rate of ploughing the circular field)

Total cost of ploughing = $3850 \times 0.5$= Rs. 1925.

Therefore, Option C is correct.

Note - In these types of problems, simply a common parameter(which is radius here) is calculated from the given data which will help to relate between the two processes which are fencing(circumference based) and ploughing(area based).

View Notes
Meaning of Cost, Costing and Cost Accounting  Cost Control and Cost Reduction  Cost Centre and Cost Unit  Cost, Costing and Cost Accounting  The Sermon at Benares Summary  Calculating the Value of an Electric Field  Perimeter and Area  Area and Perimeter  Difference Between Fixed Cost and Variable Cost  Determinant to Find the Area of a Triangle  