Areas Related to Circles Question - CBSE_BOARD_PYQ_2026_30_7_1

Question

[Section E]

Case Study 3: Circular Agricultural Field

A circular agricultural field is to be fenced at the rate of ₹$30$ per meter. The total cost of fencing the field is ₹$6000$.

1. Find the perimeter (circumference) of the circular field. (1 Mark)
2. Find the radius of the circular field. (Take $\pi = 22/7$). (1 Mark)
3. Find the total area of the field. (2 Marks)

OR (for part 3)

3. Find the cost of ploughing the field at the rate of ₹$0.50$ per m$^2$. (2 Marks)

Accepted Answer

1. Perimeter $= 6000 / 30 = 200$ m. [1.0 Mark]

2. $2\pi r = 200 \Rightarrow 2\left(\dfrac{22}{7} ight)r = 200 \Rightarrow r = \dfrac{350}{11} \approx 31.8$ m. [1.0 Mark]

[Part 3 Main] $ ext{Area} = \pi r^2 = \dfrac{22}{7} imes \left(\dfrac{350}{11} ight)^2 = \dfrac{35000}{11} \approx 3181.8$ m$^2$. [2.0 Marks]

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[Part 3 OR Choice]
Cost of ploughing $= 3181.8 imes 0.50 = ₹1590.90$. [2.0 Marks]

Question:

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