## Core Concept
The Trench method of sanitary landfill involves digging trenches for waste disposal. The area required for a landfill can be estimated based on the volume of waste generated and the depth of the landfill pit. For a given population, the amount of waste generated per day and the desired lifespan of the landfill influence the required area.

## Why the Correct Answer is Right
To calculate the area required, we first need to estimate the volume of waste generated per year. Assuming an average waste generation rate of 0.5 kg/person/day and a density of waste as 500 kg/m³ (which can vary), for a population of 10,000:
- Daily waste generation = 10,000 * 0.5 kg = 5,000 kg or 5 tons
- Annual waste generation = 5 tons/day * 365 days = 1,825 tons/year
Given the density of waste (500 kg/m³), the volume of waste per year is:
- 1,825 tons/year / 0.5 tons/m³ = 3,650 m³/year
For a landfill pit of 2m depth:
- Area required per year = Volume of waste per year / Depth of landfill = 3,650 m³/year / 2 m = 1,825 m²/year

## Why Each Wrong Option is Incorrect
- **Option A:** This option suggests an area that seems too small for the population and waste generation considered.
- **Option B:** Similarly, this seems too small without exact calculation but let's assume it's less than what we calculated.
- **Option D:** This would imply a much larger area than necessary based on our rough estimates.

## Clinical Pearl / High-Yield Fact
A key point to remember is that waste management strategies, including landfill design, must consider not just the volume of waste but also environmental and health impacts. The Trench method is one of several approaches to sanitary landfilling.

**Correct Answer:** B. 1825m²