# converting units of measurement

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• Aug 23rd 2010, 11:19 PM
larryboi7
converting units of measurement
an olympic size pool is 50.0m long 25.0 m wide. a) how many gallons of water(d = 1.0g/mL) are needed to fill the pool to an average depth of 4.8ft? b) what is the mass (in kg) of water in the pool?

Do I ever use the density formula in this?
• Aug 24th 2010, 01:01 AM
Educated
No. Since Water has a density of 1.0g/mL, you do not need to use the density formula. You CAN use it, but it would be pointless.

Eg.
Density * Volume = mass
$\displaystyle 1.0g/mL * mL = g$

Since density = 1, then Volume = mass
• Aug 24th 2010, 10:12 AM
earboth
Quote:

Originally Posted by larryboi7
an olympic size pool is 50.0m long 25.0 m wide. a) how many gallons of water(d = 1.0g/mL) are needed to fill the pool to an average depth of 4.8ft? b) what is the mass (in kg) of water in the pool?

Do I ever use the density formula in this?

But of course you must use the units!

From the definition of density:

$\displaystyle density = \dfrac{mass}{volume}$

you'll get the mass by

$\displaystyle mass = density \cdot volume$

Since 4.8' = 1.46304 m you'll get the volume of the pool as:

$\displaystyle V = 50\ m \cdot 25\ m \cdot 1.46304\ m = 1,828.8\ m^3 = 1.8288\cdot 10^9\ ml$

Then the mass is

$\displaystyle m = 1\ \frac g{ml} \cdot 1.8288\cdot 10^9\ ml = 1.8288\cdot 10^9\ g = 1.8288\cdot 10^6\ kg$