To solve this problem step by step:

Problem Breakdown:

1. Circular Plot's Radius: $R = 42 \, \text{m}$.
2. Width of the Road: $w = 3.5 \, \text{m}$.
3. New Inner Radius after subtracting road: $r = R - w = 42 - 3.5 = 38.5 \, \text{m}$.
4. Cost per square meter to pave the road: ₹45.

We will calculate:

1. Area of the road.
2. Cost of paving the road.

Step 1: Formula for Area of the Road

The area of the road is the difference between the area of the outer circle (plot) and the inner circle: $\text{Area of the Road} = \pi R^2 - \pi r^2$ Factoring $\pi$: $\text{Area of the Road} = \pi (R^2 - r^2)$

Step 2: Substitute Values

Outer radius $R = 42$, inner radius $r = 38.5$: $\text{Area of the Road} = \pi \left( 42^2 - 38.5^2 \right)$ $\text{Area of the Road} = \pi \left( 1764 - 1482.25 \right)$ $\text{Area of the Road} = \pi (281.75)$

Using $\pi \approx 3.1416$: $\text{Area of the Road} \approx 3.1416 \times 281.75 = 885.04 \, \text{m}^2$

Step 3: Cost of Paving

$\text{Cost of Paving} = \text{Area of the Road} \times \text{Cost per m}^2$ $\text{Cost of Paving} = 885.04 \times 45 = ₹39,826.80$

Final Answers:

1. Area of the Road: $885.04 \, \text{m}^2$.
2. Cost of Paving the Road: ₹39,826.80.

Do you want further explanation or calculations?

Here are related questions for practice:

1. What is the area of a circular plot with a radius of 50 m?
2. If the cost per square meter for paving is ₹60, how does it change the total cost in this case?
3. What would be the area of the road if the road's width was doubled?
4. How does the area formula for a ring-like road derive from the circle's area formula?
5. If the radius were in kilometers, how would the answer change?

Tip: Always verify whether the width of a road is added to or subtracted from the radius depending on the problem!