# It is known that 1 gallon of water weighs 8.3453 pounds. which weighs more an ounce of pennies or an ounce(as capacity) of water explain.?

Jul 19, 2018

#### Answer:

The weight of a fluid ounce of the water is $1.04316 \text{ oz}$ and
the weight of an ounce of pennies would be $1 \text{ oz}$.

#### Explanation:

I assume "ounce(as capacity)" refers to "fluid ounce" -- the unit of volume.

A conversion can be done between fluid ounce and gallon":

1 cancel(oz_"fl") * (1 cancel("cup"))/(8 cancel(oz_"fl")) * (1 cancel("qt"))/(4 cancel("cups")) * "1 gal"/(4 cancel("qt")) = 0.0078125 " gal"

From the given data, we can say that the density of water is

"density" = (8.3453 " pounds")/(gal)

It will be convenient for this problem to convert that to units of $\frac{o z}{g a l}$. Note that $o z$ without the $f l$ subscript, is weight -- not volume.

(8.3453 cancel(" pounds"))/(gal) * (16 " oz")/(1 cancel(" pound"))= (133.52" oz")/(gal)

Now that we have the density of water in $\frac{o z}{g a l}$, we can now calculate the weight of a fluid ounce of the water. (Remember that we found that $1 \text{ oz"_"fl}$ is equivalent to $0.0078125 \text{ gal}$).

(133.52" oz")/(1cancel("gal")) * 0.0078125 cancel("gal")= 1.04316 " oz"

I also refer you to this website:
https://metric-calculator.com/converter_fl_oz_to_lb.htm

At the very bottom of the page it tells you "Please note this is volume to weight conversion, this conversion is valid only for pure water at temperature 4 °C."

The density of water varies with temperature -- it is maximum at 4 °C. I suspect that at some warmer temperature, $1 \text{ oz"_"fl}$ would weigh $1 \text{ oz}$ exactly.

I hope this helps,
Steve