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Chapter 1: Problem 75

In the United States, volume of irrigation water is usually expressed in acre- feet. One acre-foot is a volume of water sufficient to cover 1 acre of land to a depth of 1 ft \(\left(640 \text { acres }=1 \mathrm{mi}^{2} ; 1 \mathrm{mi}=5280 \mathrm{ft}\right)\) The principal lake in the California Water Project is Lake Oroville, whose water storage capacity is listed as \(3.54 \times 10^{6}\) acre-feet. Express the volume of Lake Oroville in (a) cubic feet; (b) cubic meters; (c) U.S. gallons.

Short Answer

Expert verified
The volume of Lake Oroville is approximately \( 1.54 \times 10^{11} \) cubic feet, \( 4.36 \times 10^{9} \) cubic meters, and \( 1.15 \times 10^{12} \) U.S. gallons.

Step by step solution

01

Determine the conversion factor for 1 acre-foot to cubic feet

Use the given information to calculate how many cubic feet are in an acre-foot. Since 1 acre is \( \frac{1}{640} \) of a square mile and 1 square mile is \( 5280^2 \) square feet, an area of 1 acre is equivalent to \( \frac{1}{640} \times \(5280^2) \) square feet, which equals to 43560 square feet. Since 1 acre-foot is a volume covering this area to a depth of 1 foot, therefore, 1 acre-foot corresponds to a volume of 43560 cubic feet.
02

Convert Lake Oroville volume to cubic feet

Use the conversion factor obtained in step 1 to convert the volume of Lake Oroville from acre-feet to cubic feet. Since Lake Oroville has a volume of \( 3.54 \times 10^6 \) acre-feet, its volume in cubic feet is \( 3.54 \times 10^6 \times 43560 \) cubic feet.
03

Convert the volume to cubic meters

To convert cubic feet to cubic meters, use the conversion factor of 1 cubic meter equals 35.31 cubic feet. Therefore, the volume of Lake Oroville in cubic meters is \( \frac{3.54 \times 10^6 \times 43560}{35.31} \) cubic meters.
04

Convert the volume to U.S. gallons

To convert cubic feet to U.S. gallons, use the conversion factor of 1 cubic foot equals 7.48 U.S. gallons. Therefore, the volume of Lake Oroville in U.S. gallons is \( 3.54 \times 10^6 \times 43560 \times 7.48 \) U.S. gallons.

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