91Ó°ÊÓ

The volume of fluid that filled the bottle is 193 us gallons .

The rate of flow of water is 18 g/min.

Density of density of water is 1000 kg/m³.

factor for converting the US gallons to cubic centimeters.

The expression for the density is given as follows:

$\mathrm{ÒÏ}=\frac{m}{v}$ … (i)

Here, $\mathrm{ÒÏ}$is the density, m is the mass and v is the volume.

Using the converted values, find the shortfall.

First, 193 US Gallons convert into cm³.

1 US Gallons = 3785.4cm³

$$\begin{gathered} 93USGallons=93USGallons×\left(\frac{3785.4c{m}^3}{1gallon}\right) \\ =730582.2c{m}^2 \end{gathered}$$

Subtracting it from to get amount of water.

1000,000-730582.2 =269,417.8cm³

Thus, it is 269,417.8 cm³ short of 1 million cm³ .

Now to find how long it takes to fill the bottle, convert the volume into m^3..

The conversion factor for

$1c{m}^3=1×{10}^{-6}{m}^3$to m³.

Use the conversion factor to convert

^{role="math" localid="1651656536091" $$\begin{gathered} 730,582.2c{m}^{3}into{m}^3 \\ 730,582.2c{m}^3=730,582.2c{m}^3\frac{1×{10}^{-6}{m}^3}{1c{m}^3} \\ =0.7305822m^3 \end{gathered}$$}

So, volume of water in cubic meter is $0.7305822m^3$.

$$\begin{gathered} \text{Usingequation(i),themassofwateriscalculatedasfollows:} \\ m=\mathrm{ÒÏ}×v \\ =1000kg/m^3×0.7305822m^3 \\ =7305822kg \\ \text{So,themassofwaterfilledis}7305822kg. \end{gathered}$$

$$\begin{gathered} \text{Now,convertthe1.8gm/minrateintokg/min} \\ 1gm=0.001kg \\ \left(1.8\frac{g}{min}\right)\left(\frac{0.001kg}{1gm}\right)=0.0018\frac{kg}{min} \\ \text{Thetimerequiredtofillthebottleiscalculatedas} \\ t=\frac{730,5822kg}{0.0018{\displaystyle \frac{kg}{min}}} \\ =405,879min \\ \text{:Thus,itwilltake}405,879min\text{tofillthebottle.} \end{gathered}$$