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.?

1 Answer
Jul 19, 2018

Answer:

The weight of a fluid ounce of the water is # 1.04316 " oz"# and
the weight of an ounce of pennies would be #1 " 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 #(oz)/(gal)#. Note that #oz# without the #fl# 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 #(oz)/(gal)#, we can now calculate the weight of a fluid ounce of the water. (Remember that we found that #1 " oz"_"fl"# is equivalent to #0.0078125 " 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" oz"_"fl"# would weigh #1 " oz"# exactly.

I hope this helps,
Steve