Chapter 1, Problem 44GP

To determine

To find: Metric tons of water fell on the city and the number of gallons of water.

Answer to Problem 44GP

  $4\times {10}^5\text{ tons}$ of water fell on the city which is equal to $1.05\times {10}^8\text{ gallons}$

Explanation of Solution

Given:

Dimension of city = $8\text{ km}\times 5\text{ km}$

Rain fall $=1{\text{ cm = 10}}^5\text{km}$

Time $=2\text{ h}$

Formula used:

Volume is,

  $V=\text{Length}\times \text{Width}\times \text{height}$

Calculation:

Volume of the water is,

  $\begin{array}{l}V=1\times \left(5\times {10}^3\times 100\right)\times \left(8\times {10}^3\times 100\right)\\ V=40\times {10}^{10}{\text{ cm}}^3\end{array}$

It is given that $1{\text{cm}}^3$ water has a mass of 1 gram or ${10}^{-3}\text{kg}$

So, mass of water in volume can be given as:

  $\begin{array}{c}M=40\times {10}^{10}\times {\text{10}}^{-3}\text{ kg}\\ M=40\times {10}^7\text{ kg}\\ \text{=}40\times {10}^7\text{kg}\times \frac{1\text{metric}\text{ton}}{{10}^3\text{kg}}\\ =4\times {10}^5\text{metric tons}\end{array}$

Water in gallon is,

  $\begin{array}{l}V=\frac{40\times {10}^7}{3.78}\\ V=1.05\times {10}^8\text{ gal}\end{array}$

Conclusion:

Water fell on the city is $4\times {10}^5\text{ tons}$

Volume in gallon is

  $V=1.05\times {10}^8\text{ gal}$