# $

{\text{The cost of fencing a circular field at the rate Rs 24 per metre is Rs 5280}}{\text{. The field is to be }} \\

{\text{ploughed at the rate of Rs}}{\text{. 0}}{\text{.50 per }}{{\text{m}}^2}.{\text{ Find the cost of ploughing the field}}{\text{. (Take }}\pi {\text{ = }}\dfrac{{22}}{7}{\text{) }} \\

{\text{A}}{\text{. Rs 1278}} \\

{\text{B}}{\text{. Rs 1437}} \\

{\text{C}}{\text{. Rs 1925}} \\

{\text{D}}{\text{. Rs 2870}} \\

$

Last updated date: 18th Mar 2023

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\[

{\text{Given, Total cost of fencing the circular field }} = {\text{Rs }}5280 \\

{\text{Rate of fencing the circular field = Rs 24/m}} \\

{\text{Rate of ploughing the circular field = Rs 0}}{\text{.5/}}{{\text{m}}^2} \\

{\text{Since, we know that fencing occurs around the circumference and ploughing is }} \\

{\text{done on the area of the circular field}}{\text{.}} \\

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

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

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

{\text{So, the radius of the circular field is 35 metres}}{\text{.}} \\

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

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

\Rightarrow {\text{Total cost of ploughing = 385}}0 \times 0.5 = {\text{Rs }}1925. \\

{\text{Therefore, Option C is correct}}{\text{.}} \\

\\

{\text{Note - In these type of problems, simply a common parameter(which is radius here) is calculated }} \\

{\text{from the given data which will help to relate between the two processes which are }} \\

{\text{fencing(circumference based) and ploughing(area based)}}{\text{. }} \\

\]

{\text{Given, Total cost of fencing the circular field }} = {\text{Rs }}5280 \\

{\text{Rate of fencing the circular field = Rs 24/m}} \\

{\text{Rate of ploughing the circular field = Rs 0}}{\text{.5/}}{{\text{m}}^2} \\

{\text{Since, we know that fencing occurs around the circumference and ploughing is }} \\

{\text{done on the area of the circular field}}{\text{.}} \\

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

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

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

{\text{So, the radius of the circular field is 35 metres}}{\text{.}} \\

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

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

\Rightarrow {\text{Total cost of ploughing = 385}}0 \times 0.5 = {\text{Rs }}1925. \\

{\text{Therefore, Option C is correct}}{\text{.}} \\

\\

{\text{Note - In these type of problems, simply a common parameter(which is radius here) is calculated }} \\

{\text{from the given data which will help to relate between the two processes which are }} \\

{\text{fencing(circumference based) and ploughing(area based)}}{\text{. }} \\

\]

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