Question

The cost of fencing a circular
field at the rate of ₹24 per meter is ₹5280.Find the radius of field
​

Answer 1

$\mathbb{SOLUTION:-}$

★ Given,

• Rate of fencing = ₹24/m.
• Cost of fencing the circular field = ₹5280
• Find the radius

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We know that, it costs ₹5280 to fence the whole field.

So, we can find out the circumference of the circle by dividing the total cost of fencing by the rate of fencing per m.

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$\begin{gathered}\\\;\sf{:\rightarrow\;\;circumference\;=\;\bf{\dfrac{5280}{24}\:}}\end{gathered}$

$\: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;circumference=\;\bf{{ \sf{\cancel\dfrac{5280}{24}}}\:}} = 220\end{gathered}$

$\: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;circumference\;=\;\bf{{220 {m} }\:}}\end{gathered}$

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Now we get the circumference i.e., 220m.

Now we are asked to find the radius of the field.

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Formula using here,

$\: \: \: \: \: \: \: \: {\sf { \blue{ \boxed{ \sf {2\pi \:r \: = \: circumference}}}}}$

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★ Where,

• We are taking π as 22/7
• Circumference = 220m
• let's assume x as radius.

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Putting down the values,

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$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{2 \times \dfrac{22}{7} \times x = 220\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{\dfrac{44}{7} \times x = 220\:}}\end{gathered}$

Here I'm transposing LHS to RHS (while transposing the terms sign changes inversely).

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{ x = \frac{ 220 \times 7}{44} \:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{ x = \frac{1540}{44} \:}}\end{gathered}$

$\: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;x=\;\bf{{ \sf{\cancel\dfrac{1540}{44}}}\:}} = 35\end{gathered}$

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Thus, the radius of circular field is 35m.

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★ Formulas related to circle:-

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• Circumference of circle = 2πr

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• Area of circle = πr²

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• Circumference of semi-circle = πr

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• Area of semi-circle = 1/2 (πr²).