Textbook Question
Perform the following calculations with the correct number of significant figures.
5.1125 + 0.67 + 3.2
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1. Intro to Physics Units
Operations with Significant Figures
Problem 62
Textbook Question
An average family of four uses roughly 1200 L (about 300 gallons) of water per day (1L = 1000 cm³). How much depth would a lake lose per year if it covered an area of 60 km² with uniform depth and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation, rain, creeks and rivers.
Verified step by step guidance1
Calculate the total volume of water used by the town in one day. Multiply the daily water usage per family by the number of families in the town. Given that each family of four uses 1200 L per day, first find the number of families by dividing the town's population by four.
Convert the daily water usage from liters to cubic meters for easier calculation with the lake's dimensions, knowing that 1 cubic meter (m³) equals 1000 liters.
Calculate the total volume of water used by the town in one year by multiplying the daily volume usage by 365 days.
Convert the area of the lake from square kilometers to square meters to match the units of the volume calculation. Recall that 1 square kilometer equals 1,000,000 square meters.
Determine the depth the lake would lose per year by dividing the annual volume of water used by the area of the lake. This will give the depth in meters.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Volume and Depth Relationship
The relationship between volume, area, and depth is fundamental in fluid mechanics. The volume of water can be calculated using the formula V = A × d, where V is volume, A is area, and d is depth. This concept helps in determining how much depth a body of water will lose when a certain volume is extracted.
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Water Consumption Calculation
Understanding water consumption is crucial for this problem. The average daily water usage per person can be multiplied by the population to find the total daily water consumption. This total can then be converted into an annual figure to assess the impact on the lake's depth over time.
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Area Conversion
Converting units is essential for accurate calculations. In this case, the area of the lake is given in square kilometers, which needs to be converted to square centimeters to match the volume units. Knowing that 1 km² equals 10^10 cm² is vital for ensuring consistency in calculations.
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