Discussion
The circumference of a circular ground is 88 meters. A strip of land, 3 meters wide, inside and along the circumference of the ground is to be levelled. What is the budgeted expenditure if the levelling costs is Rs. 7 per square meter
Answer: A
The expenditure is Rs. 1650.
From the circumference, \(2\pi R = 88\), so \(R = 14\) m. The strip runs inside the boundary, so the inner radius is \(14 - 3 = 11\) m, and the strip is the ring between them:
\[ \begin{aligned} \text{area} &= \tfrac{22}{7}(14^{2} - 11^{2}) \\ &= \tfrac{22}{7} \times 75 = \tfrac{1650}{7}\ \text{m}^{2} \end{aligned} \]
At Rs. 7 per square metre the cost is \(\tfrac{1650}{7} \times 7 = 1650\). Taking the strip outside the circle (radius 17 m) gives a larger area and a cost of 2046, close to the 2050 offered, which is the trap.
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