Answer

Verified

456k+ views

\[

{\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{. }} \\

\]

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE