Question

A bottle with a volume of 193 U. S. fluid gallons is filled at the rate of 1.9 g/min. (Water has a density of 1000 kg/m3, and 1 U.S. fluid gallon = 231 in.3.) How long does the filling take?

Answer 1

Answer:

0.732 years

Explanation:

We are given that

Volume of fluid filled in bottle=193 U.S

1 U.S fluid  gallon=231 cubic inch

193 U.S gallon=$231\times 193=44583in^3$

$1 in^3=1.63871\times 10^{-5}m^3$

$44583in^3=44583\times 1.63871\times 10^{-5}=0.731m^3$

Density of water=$1000kg/m^3$

Mass=$Volume\times density$

Using the formula

Mass=$0.731\times 1000=731kg$

1kg =1000g

$731kg=731\times 1000=731\times 10^3g$

By using $1000=10^3$

1.9 g of fluid takes time to fill in the bottle=1 min

1 g of fluid takes time to fill in the bottle=$\frac{1}{1.9}min$

$731\times 10^3$g of fluid takes time to fill in the bottle=$\frac{1}{1.9}\times 731\times 10^3$min

Time=$384.7\times 10^3$min

$1min=\frac{1}{60\times 24\times 365}$years

Time=$384.7\times 10^3\times \frac{1}{60\times 24\times 365}years$

Time =0.732 years

Hence, it takes to filling the 193 U.S fluid gallons in bottle=0.732 years