The circumference of a circular ground is 88 metres. A strip of land, 3 metres wide, inside and along the circumference of the ground is to be levelled. What is the budgeted expenditure if the levelling costs ₹ 7 per square metre?

### Concept & Area of a Circular Ring The area of a circular path (or ring) located inside a circular boundary is the difference between the area of the outer circle and the area of the inner circle. $$ \text{Area} = \pi R^2 - \pi r^2 = \pi(R^2 - r^2) $$ ### Step-by-Step Solution * **Find the outer radius (R):** The circumference is $2\pi R = 88$ m. * $2 \times \frac{22}{7} \times R = 88 \Rightarrow R = \frac{88 \times 7}{44} = 14$ m. * **Find the inner radius (r):** The strip is 3 m wide and inside, so $r = R - 3 = 14 - 3 = 11$ m. * **Calculate the area of the strip:** $\text{Area} = \pi(R^2 - r^2) = \frac{22}{7} \times (14^2 - 11^2)$ $\text{Area} = \frac{22}{7} \times (196 - 121) = \frac{22}{7} \times 75$ sq m. * **Calculate the cost:** $\text{Total Cost} = \text{Area} \times \text{Rate} = \left(\frac{22}{7} \times 75\right) \times 7$ $\text{Total Cost} = 22 \times 75 = 1650$. ### Exam Strategy & Shortcut Notice that the cost calculation involves multiplying by 7, which perfectly cancels out the denominator of $\pi$ ($\frac{22}{7}$). Delaying the multiplication of $\frac{22}{7} \times 75$ saves time since the 7s cancel out in the final step. ### Common Pitfall A common mistake is adding the width to the radius instead of subtracting it, assuming the path is outside the ground when the problem explicitly states it is "inside". ### Final Answer Therefore, the correct answer is **₹ 1650**.