Question

Lake Mead was created by Hoover Dam (aka Boulder Dam) on the border between Arizona and Nevada. Suppose all 31,250,000 acre-feet of the water in this lake suddenly flooded the Mojave Desert, which has an area of 15,000 square miles. How deep (in inches) would the water be?

Answer 1

The water from Lake Mead would create a depth of approximately 29.16 inches if it flooded the Mojave Desert, which is calculated by converting both the volume of Lake Mead and the area of the Mojave Desert to cubic inches and square inches, respectively.

Step-by-step explanation:

The student asks how deep the water from Lake Mead would be if it flooded the Mojave Desert. To find the depth in inches, we first need to convert the volume of water in Lake Mead from acre-feet to cubic feet and then to cubic inches. Next, we convert the area of the Mojave Desert from square miles to square inches. The depth is then calculated by dividing the total volume in cubic inches by the area in square inches.

First, we convert 31,250,000 acre-feet to cubic feet by multiplying by the number of cubic feet in one acre-foot:

1. 31,250,000 acre-feet * 43,560 cubic feet/acre-foot = 1,361,250,000,000 cubic feet.
2. Convert square miles to square inches:
3. 15,000 square miles * (5280 feet/mile)^2 * (12 inches/foot)^2 = 5,559,520,000,000,000 square inches.
4. Divide the volume by the area:
5. 1,361,250,000,000 cubic feet * 12^3 cubic inches/cubic foot ÷ 5,559,520,000,000,000 square inches = 29.16 inches.

Therefore, if Lake Mead's water volume were to flood the Mojave Desert, it would result in a depth of approximately 29.16 inches.