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 \(1 \mathrm{ft}\). An acre is \(4840 \mathrm{yd}^{2}\). 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? (b) How much would it cost one household per day if it were the only source of water?

Short Answer

Expert verified
The cost per liter of desalinated water is approximately $0.00158/liter, and the daily cost per household for using desalinated water as the only source is about $2.67 per day.

Step by step solution

01

Convert acre to square meters

First, we need to convert an acre to square meters. We know that an acre is 4840 square yards. To convert it to square meters, we use the fact that 1 yard = 0.9144 meters. 1 acre = 4840 sq.yards * (0.9144 m/yd)^2 1 acre = 4840 * (0.9144)^2 sq.meters 1 acre ≈ 4046.86 sq.meters
02

Calculate volume in acre-feet

Now we will find the volume of water in an acre-foot. Since the depth is 1 foot and 1 foot is equal to 0.3048 meters, we have: Volume = Area * Depth Volume = 4046.86 sq.meters * 0.3048 meters Volume ≈ 1233.49 cubic meters
03

Convert cubic meters to liters

We need to convert the volume to liters. We know that 1 cubic meter = 1000 liters. Volume in liters = 1233.49 cubic meters * 1000 liters/cubic meter Volume in liters ≈ 1,233,490 liters
04

Calculate the cost per liter

Now we can find the cost of desalinated water per liter. The cost per acre-foot is given as $1950. Cost per liter = \(\frac{1950}{1233490}\) dollars/liter Cost per liter ≈ \(0.00158\) dollars/liter
05

Calculate the daily cost per household

We know that one acre-foot of water can supply two households for a year. So, to find the cost per household per day, we will divide the cost per acre-foot by 2 (number of households) and then by 365 (days in a year). Cost per household per day = \(\frac{1950}{2 \times 365}\) dollars/day Cost per household per day ≈ $2.67/day The cost per liter of desalinated water is approximately \(0.00158/liter, and the daily cost per household for using desalinated water as the only source is about \)2.67 per day.

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