What mass of water fell on the town in Problem 7? Water has a density of${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{\times }\mathbf{}\mathbf{kg}\mathbf{/}{\mathbf{m}}^{\mathbf{3}}}$.

Area of the town is ${}^{\mathbf{26}\mathbf{}{\mathbf{km}}^{\mathbf{2}}}$

Fall of rain is ${}^{\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{inch}}$

The density of water is ${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{}\mathbf{kg}\mathbf{/}{\mathbf{m}}^{\mathbf{3}}}$.

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors.

The expression for density is given as:

$\mathbf{density}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{volume}}$ … (i)

By converting volume into m3 and using it in relation to mass, density, and volume, you can find the mass of water that fell on the town.

From problem 7, the volume of water that fell on the town is,

$$\begin{gathered} \mathbf{V}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{26}\mathbf{}{\mathbf{km}}^{\mathbf{2}}\mathbf{)}\mathbf{(}\mathbf{2}\mathbf{}\mathbf{inch}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{(}\mathbf{26}\mathbf{}{\mathbf{km}}^{\mathbf{2}}\mathbf{)}\mathbf{.}{\mathbf{\left(}\frac{\mathbf{1000}\mathbf{}\mathbf{m}}{\mathbf{1}\mathbf{}\mathbf{km}}\mathbf{\right)}}^{\mathbf{2}}\mathbf{.}\mathbf{}\mathbf{(}\mathbf{2}\mathbf{}\mathbf{inch}\mathbf{)}\mathbf{.}\mathbf{}\mathbf{\left(}\frac{\mathbf{0}\mathbf{.}\mathbf{0254}}{\mathbf{1}\mathbf{}\mathbf{inch}}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{26}\mathbf{}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{}{\mathbf{m}}^{\mathbf{2}}\mathbf{)}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{0508}\mathbf{}\mathbf{m}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{}{\mathbf{m}}^{\mathbf{3}} \end{gathered}$$

Thus, the volume of the water is ${}^{\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{}{\mathbf{m}}^{\mathbf{3}}}$.

Rearrange the equation (i) for mass.

$\mathbf{Mass}\mathbf{=}\mathbf{Density}\mathbf{\times }\mathbf{Voulme}$

Substitute the given values to calculate the mass.

$$\begin{gathered} \mathbf{Mass}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{}\frac{\mathbf{kg}}{{\mathbf{m}}^{\mathbf{3}}}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{}{\mathbf{m}}^{\mathbf{3}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{}\mathbf{kg} \end{gathered}$$

Thus, the mass of the water that fell on the town is${}^{\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{}\mathbf{kg}}$.