Question

The cost of fencing a circular field at the rate of Rs.24 per metre is Rs. 5280.

Find the radius of the field.​

Answer 1

$\LARGE\textbf{\underline{\underline{Given :-}}}$

• Cost of fencing a circular field per meter = Rs. 24 .
• Total cost of fencing the circular field = Rs. 5280 .

$\LARGE\textbf{\underline{\underline{To find :-}}}$

• The radius of the circular field .

$\LARGE\textbf{\underline{\underline{Method :-}}}$

• As we know the fencing is put edge of of any area or field . And that edge is the perimeter of that of that area or field .

• So , in this question the perimeter of the circular field is the circumference of the circular field .

• And we have the total cost and the per meter cost of the fencing . So , by dividing the total cost by the per meter cost we can get the total length of the fencing or the circumference of the circular field.

$\LARGE\textbf{\underline{\underline{Formula :-}}}$

$\large\boxed{\textbf\textcolor{orange}{➛\: \: \: \: Circumference of the circle = 2 \pi r }}$

$\LARGE\textbf{\underline{\underline{Solution :-}}}$

* Total cost of the fencing ÷ Cost of the per meter fencing = Total length covered by the fencing .

$\large\textsf{➙\: \: \: \: \: \: Total length of the fencing = \cancel \cfrac{5280}{24} }$

$\large\textsf{➙\: \: \: \: \: \: Total length of the fencing = 220 m }$

So , the length covered by the fencing or the circumference of the circular field = 220 m

• By using the formula of the circumference of the circle :-

➩ Here : -

• Circumference = 220 m .
• π = 22/7

$\large\Longrightarrow\textsf{\: \: \: \: 220 = 2 × \cfrac{22}{7} × r }$

$\large\Longrightarrow\textsf{ \: \: \: \: \cfrac{220 × 7 }{22 × 2 } = r}$

$\large\Longrightarrow\textsf{ \: \: \: \: \cancel\cfrac{1540}{44} = r }$

$\large\Longrightarrow\textsf{\: \: \: \: 35 = r }$

$\large\boxed{\therefore\textbf\textcolor{red}{The radius of the circular field = 35 m }}$

$\LARGE\textbf{\underline{\underline{Formulas:-}}}$

• Of a circle :-

$\large\textbf\textcolor{purple}{↦\: \: \: \: Area = π r²}$

$\large\textbf\textcolor{purple}{↦\: \: \: \: Radius ( r ) = \cfrac{1}{2} × D }$

$\large\textbf\textcolor{purple}{↦\: \: \: \: Diameter ( D ) = 2r}$

Answer 2

$\huge\mathfrak{ \blue{\underline{\underline{Solution :}}}}$

Total cost of the fencing ÷ Cost of the per meter fencing = Total length covered by the fencing .

$\textsf{➙ \: Total length of the fencing = \cancel \cfrac{5280}{24} } \\\textsf{➙ \: Total length of the fencing = 220 m }$

So , the length covered by the fencing or the circumference of the circular field =220 m

Using the formula of the circumference of the circle :

➩ Here : -

• Circumference = 220 m .
• π = 22/7

$\large\Longrightarrow\text{\: \: \: \: 220 = 2 × \cfrac{22}{7} × r } \\ \\ \large\Longrightarrow\textsf{ \: \: \: \: \cfrac{220 × 7 }{22 × 2 } = r} \\ \\ \large\Longrightarrow\textsf{ \: \: \: \: \cancel\cfrac{1540}{44} = r } \\ \\ \large\Longrightarrow\text{ \purple{\: \: \: \: 35 = r }}$

$\large {\text{ \red{\boxed{\therefore{The \: radius \: of \: the \: circular \: field = 35 m }}}}}$