Mass/Density problem - please check my working.

[bentleyq]

1. An olympic pool is 50m long 25m wide and a minimum average depth of 2m
a) If the pool is filled as specified, what is the mass of water? Denisty of water to be 1.0g/cm^3
b) How long will it take to fill the pool from a standard garden hose, if the flow rate from hose has average of 8 liters per minute?




2. Homework Equations (density = mass/volume)(volume = LxWxH)



3. a) Volume = 25 x 50 x 2 = 2500m^3
Convert density to kg/m^3, 1g/cm^3 = 1000kg/m^3
mass = 2500 x 1000 = 2.5e5kg

b) I just did m^3 into liters, so 2500m^3 = 2.5e5liters
2.5e5/8
=312500min approx 217 days


I know its basic question, with unit conversation etc, but I have no answers to check my working. Thanks

 

[cepheid]

Welcome to PF bentleyq!

1. An olympic pool is 50m long 25m wide and a minimum average depth of 2m
a) If the pool is filled as specified, what is the mass of water? Denisty of water to be 1.0g/cm^3
b) How long will it take to fill the pool from a standard garden hose, if the flow rate from hose has average of 8 liters per minute?




2. Homework Equations (density = mass/volume)(volume = LxWxH)



3. a) Volume = 25 x 50 x 2 = 2500m^3
Convert density to kg/m^3, 1g/cm^3 = 1000kg/m^3
mass = 2500 x 1000 = 2.5e5kg

b) I just did m^3 into liters, so 2500m^3 = 2.5e5liters
2.5e5/8
=312500min approx 217 days


I know its basic question, with unit conversation etc, but I have no answers to check my working. Thanks

Check your arithmetic. 2500 * 1000 = 2.5e6. You're too low by a factor of 10.

Your conversion to litres is also similarly wrong.

 

[bentleyq]

Ah thanks, i should be 2.5e6liters also, but seems i still have the correct time of 312500min?

 

[cepheid]

Ah thanks, i should be 2.5e6liters also, but seems i still have the correct time of 312500min?

Looks okay to me! EDIT: your answer for the time, I mean.

 

[Nickie]

Your calculations for the mass of water in the Olympic pool are correct. The density of water is commonly known to be 1.0g/cm^3, but it is important to remember to convert to the appropriate units for consistency. Great job on that!

For part b, your approach is correct. However, your final answer of 217 days seems very long. This could be due to an error in unit conversion or calculation. Double check your numbers and make sure you are using the correct units. Also, make sure you are converting from minutes to hours or days for the final answer. It should not take that long to fill an Olympic pool with a standard garden hose.

Overall, your working is good and it is important to double check your calculations and units to ensure accuracy in your results. Keep up the good work!