In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly 1 ft. An acre is 4840 yd2. An acre-foot is enough water to supply two typical households for 1.00 yr. (a) If desalinated water costs \$1950 per acre-foot, how much does desalinated water cost per liter?

Verified step by step guidance

1. Convert the area of an acre from square yards to square feet using the conversion factor: 1 yard = 3 feet. Therefore, 1 acre = 4840 yd^2 * (3 ft/yd)^2.
2. Calculate the volume of water in cubic feet for 1 acre-foot by multiplying the area in square feet by the depth of 1 foot.
3. Convert the volume from cubic feet to cubic inches using the conversion factor: 1 cubic foot = 12^3 cubic inches.
4. Convert the volume from cubic inches to liters using the conversion factor: 1 liter = 61.024 cubic inches.
5. Calculate the cost per liter by dividing the cost per acre-foot (\$1950) by the volume in liters.

Key Concepts

Volume Conversion

To solve the problem, it's essential to understand how to convert acre-feet into liters. An acre-foot is a unit of volume that represents the amount of water needed to cover one acre to a depth of one foot. Knowing the conversion factors between these units is crucial for calculating the cost per liter.

Cost Calculation

The question requires calculating the cost of desalinated water per liter based on the total cost per acre-foot. This involves dividing the total cost by the total volume in liters, which allows for a clear understanding of the price per unit volume of water.

Desalination Economics

Understanding the economics of desalination is important, as it provides context for the cost of water. Desalination is a process that converts seawater into freshwater, and the cost of this process can vary significantly based on technology, energy use, and local conditions, influencing the price per acre-foot.