East Battle Lake in Minnesota covers an area of about 1950 acres or 8.5X10^7 square feet and its average depth is about 3.2x10^1 feet.
a. Estimate the cubic feet of water in the lake. (hint: Volume=area x average depth.)
b. One cubic foot of water equals about 7.5 gallons. How many gallons of water are in this lake?
c. The population of the US is about 3.02 X 10^8, and the average American uses about 1.5x10^2 gallons of water per day. Could this lake supply the American population with water for 1 day?
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Volume = area * depth
= 1950 acres * 32'
= 1950*4840*9 sq.ft * 32'
= 2.718 * 10^9 cubic ft.
= 2.038 * 10^10 gal.
Water usage per day
= population * 150 gal / day
= 3.02*10^8 * 150
= 4.53 * 10^10 gal/day
Since 2.038*10^10 < 4.53*10^10, the conclusion is:______________________
The population of the US is about 3.02 X 10^8, and the average American uses about 1.5x10^2 gallons of water per day. Could this lake supply the American population with water for 1 day?
a. To estimate the cubic feet of water in the lake, we can use the formula Volume = Area x Average Depth. Given that the area of East Battle Lake is approximately 8.5 x 10^7 square feet and the average depth is about 3.2 x 10^1 feet, we can substitute these values into the formula:
Volume = (8.5 x 10^7 square feet) x (3.2 x 10^1 feet)
= 2.72 x 10^9 cubic feet
Therefore, the estimated volume of water in the lake is approximately 2.72 x 10^9 cubic feet.
b. Now, to convert cubic feet to gallons, we are given that 1 cubic foot of water equals about 7.5 gallons. So, we can calculate the number of gallons in the lake by multiplying the volume in cubic feet by the conversion factor:
Number of gallons = (2.72 x 10^9 cubic feet) x (7.5 gallons/cubic foot)
= 2.04 x 10^10 gallons
Hence, there are approximately 2.04 x 10^10 gallons of water in the lake.
c. To determine if this lake could supply the American population with water for 1 day, we need to calculate the total water usage of the American population for 1 day. Given that the population of the US is about 3.02 x 10^8 and the average American uses about 1.5 x 10^2 gallons of water per day, we can calculate the total water usage:
Total water usage = (3.02 x 10^8 people) x (1.5 x 10^2 gallons/person)
= 4.53 x 10^10 gallons
Since the total water usage for 1 day by the American population is approximately 4.53 x 10^10 gallons, and the lake contains about 2.04 x 10^10 gallons, we can conclude that East Battle Lake alone would not be sufficient to supply the American population with water for 1 day.