Question

एक वृत्ताकार खेत पर 24 रु. प्रति मीटर की दर से बाड़ लगाने का व्यय 5280 रु. है। इस क्षेत्र की 0.50 रु. प्रति वर्ग मीटर की दर
से जुताई कराई जानी है। खेत की जुताई कराने का व्यय ज्ञात कीजिए।​

Answer 1

Given:

एक वृत्ताकार खेत पर 24 रु. प्रति मीटर की दर से बाड़ लगाने का व्यय 5280 रु. है|

इस क्षेत्र की 0.50 रु. प्रति वर्ग मीटर की दर  से जुताई कराई जानी है।

To find:

खेत की जुताई कराने का व्यय ज्ञात कीजिए।​

Formulas to be used:

$\boxed{\bold{Circumference \:of\:a\:circle = 2\pi r}}\\\\\boxed{\bold{Area \:of\:a\:circle = \pi r^2}}$

Solution:

The total cost of fencing the circular field = Rs. 5280

The per meter cost of fencing the field = Rs. 24

∴ The circumference of the field = $\frac{Total \:cost}{Cost\:per\:meter} = \frac{5280}{24 } = 220 \:m$

Let "r" meter represent the radius of the circular field.

∴ $2\pi r$ = 220

$\implies 2 \times \frac{22}{7} \times r = 220$

$\implies r = \frac{220 \times7 }{2 \times 22}$

$\implies \bold{r = 35\:m}$ ← the radius of the field

∴ The area of the field is = $\pi r^2 = \frac{22}{7} \times 35^2 = 3850 \:m^2$

The cost of ploughing per meter square of the circular field is = Rs. 0.50

∴ The total cost of ploughing 3850 m² of the field is,

= Rs. 0.50 × 3850 m²

= Rs. 1925

Thus, the cost of ploughing the circular field is Rs. 1925.

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