Question: The record for the largest glass bottle was set in 1992 by a team in Millville, New Jersey—they blew a bottle with a volume of 193 U.S. fluid gallons. (a) How much short of 1.0 million cubic centimeters is that? (b) If the bottle were filled with water at the leisurely rate of 1.8 g/min, how long would the filling take? Water has a density of 1000 kg/m³_.

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:

$\rho =\frac{m}{v}$ … (i)

Here, $\rho$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

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

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

$1c{m}^3=1\times {10}^{-6}{m}^3$to m³.

Use the conversion factor to convert

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

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

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

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