An Olympic swimming pool is 164 ft long and 82 ft wide. Assume that it is filled to a depth of 3.0 m, which is the Olympic recommendation.
a. What volume of water in gal is needed to fill the pool?
b. What volume of water in L is needed to fill the pool?
c. The U.S. Geological Survey estimates that in 2015 U.S. domestic use of water was 82 gal/day per person. Using this value for daily usage, for what length of time could the water used to fill an Olympic swimming pool provide the domestic water usage for a community of 25,000 residents?

검증된 단계별 안내

Convert the dimensions of the pool from feet to meters for consistency. Use the conversion factor: 1 ft = 0.3048 m.

Calculate the volume of the pool in cubic meters using the formula: \( \text{Volume} = \text{length} \times \text{width} \times \text{depth} \).

Convert the volume from cubic meters to gallons using the conversion factor: 1 cubic meter = 264.172 gallons.

Convert the volume from cubic meters to liters using the conversion factor: 1 cubic meter = 1000 liters.

Calculate the number of days the pool's water can supply the community by dividing the total volume in gallons by the daily usage per person and then by the number of residents.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Volume Calculation

To determine the volume of the swimming pool, we need to use the formula for the volume of a rectangular prism, which is length × width × height. In this case, the dimensions must be consistent, so we will convert the depth from meters to feet or vice versa to ensure all measurements are in the same unit before performing the calculation.

Unit Conversion

Converting between different units of measurement is essential in this problem. We need to convert the volume from cubic feet to gallons and liters. Knowing the conversion factors—1 cubic foot equals approximately 7.48 gallons and 1 cubic foot equals about 28.32 liters—will allow us to accurately express the volume in the required units.

Water Usage Calculation

To find out how long the water from the pool can supply a community's daily usage, we need to calculate the total volume of water in gallons and then divide this by the daily water usage per person multiplied by the number of residents. This will give us the number of days the pool's water can sustain the community's needs.