How Many Gallons and Kilograms of Water Are Needed to Fill an Olympic-Size Pool?

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of the volume and mass of water needed to fill an Olympic-size swimming pool. Participants explore the conversion of measurements and the application of density in their calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant provides the dimensions of the pool and calculates the volume in cubic meters based on the average depth converted from feet to meters.
  • Another participant questions the need for gallons in the mass calculation and suggests converting cubic meters to milliliters or adjusting the density units instead.
  • A different participant shares their calculated answer and describes their conversion process from gallons to liters and then to milliliters, applying the density formula to find the mass in kilograms.
  • One participant reminds others to consider significant digits in their calculations.

Areas of Agreement / Disagreement

Participants express different approaches to the problem, particularly regarding the necessity of converting to gallons versus using metric units directly. There is no consensus on the correctness of the calculations presented.

Contextual Notes

Participants have not fully resolved the conversion factors or the implications of significant digits in their calculations, leaving some assumptions unaddressed.

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Homework Statement


An Olympic-size pool is 50.0 m long and 25.0 m wide.
(a) How many gallons of water (d=1.0 g/mL) are needed to fill the pool to an average depth of 4.8 ft?
(b) What is the mass (in kg) of water in the pool?


Homework Equations


density = m/V


The Attempt at a Solution


I almost got all of Part (a). Here's what I did:

4.8 ft x .3048m/ft = 1.46304 m

After converting the depth in feet to depth in meters, I multiplied:

1.46304 m x 50 m x 25 m = 1828.8 cubic meters.

From here I do not know how to get that Volume into gallons. I think it might work if I convert to cubic feet, then to gallons? Is that right? Once I have that I know all I have to do is use the density formula to get the mass. Help please!
 
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How many litres per galon? How many liter per cubic meter?

You don't need galons for the mass. What you have to do is to either convert cubic meter to mililiters or density from g/mL to kg/cubic meter.
 
oh okay I see. For an answer I got 18285.335. I found the conversions for gallons to L and then to mL anyway, and then I used that in d = m/V and converted to kg when I got my answer in g. Please let me know if this is not correct :-X thanks so much for your help!
 
Significant digits!
 

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