Problem Statement:
A circular garden with a radius of 80 meters has a pathway around and outside it, with a width of 3 meters. We need to calculate the cost of leveling the path at a rate of 7.50 rupees per square meter.

Solution:

Step 1: Calculate the area of the garden:
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
In this case, the radius of the garden is 80 meters.
So, the area of the garden can be calculated as:
A_garden = π * (80)^2

Step 2: Calculate the area of the pathway:
The pathway is outside the garden and has a width of 3 meters.
To calculate the area of the pathway, we need to subtract the area of the garden from the area of the larger circle that includes the pathway.
The radius of the larger circle will be the sum of the radius of the garden and the width of the pathway.
So, the area of the pathway can be calculated as:
A_pathway = π * (83)^2 - A_garden

Step 3: Calculate the cost of leveling the path:
The cost of leveling the path is given as 7.50 rupees per square meter.
To calculate the total cost, we need to multiply the area of the pathway by the cost per square meter.
So, the cost of leveling the path can be calculated as:
Cost = A_pathway * 7.50

Step 4: Calculate the final answer:
Using the above calculations, we can now plug in the values to find the final answer.
Final Answer = Cost

Calculations:
- Radius of the garden (r) = 80 meters
- Width of the pathway = 3 meters

- Area of the garden (A_garden) = π * (80)^2
- Area of the pathway (A_pathway) = π * (83)^2 - A_garden

- Cost = A_pathway * 7.50

- Final Answer = Cost

Final Answer:
The cost of leveling the pathway at a rate of 7.50 rupees per square meter is the Final Answer.

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