A well has to be dug out that is to be 22.5 m deep and of diameter 7m. Find the cost of plastering the inner curved surface at ₹ 3 per sq. meter.

### Concept & Area Calculation The "inner curved surface" of a well corresponds to the curved surface area (CSA) of a cylinder. CSA = $2\pi rh = \pi dh$ Total Cost = CSA $\times$ Rate per sq. meter. ### Step-by-Step Solution * **Given:** Depth (height $h$) = $22.5 \text{ m}$, Diameter ($d$) = $7 \text{ m}$, Rate = $₹3/\text{m}^2$. * Calculate the Curved Surface Area: $$\text{CSA} = \pi \times d \times h$$ $$\text{CSA} = \frac{22}{7} \times 7 \times 22.5$$ $$\text{CSA} = 22 \times 22.5 = 495 \text{ m}^2$$ * Calculate the total cost: $$\text{Cost} = \text{CSA} \times \text{Rate}$$ $$\text{Cost} = 495 \times 3 = ₹ 1485$$ ### Exam Strategy & Shortcut When the diameter is $7$ (or a multiple of 7), use the $\pi dh$ formula directly instead of converting to radius ($r = 3.5$). The $7$ in the numerator elegantly cancels the $7$ in the denominator of $\frac{22}{7}$. Then $22 \times 22.5$ can be thought of as $22 \times (45/2) = 11 \times 45 = 495$. ### Common Pitfall A common error is to calculate the total surface area (including the base) instead of just the curved surface area, leading to an overestimation of the cost. ### Final Answer Therefore, the correct answer is **₹ 1485**.