Question

A heavy rainstorm dumps 1.0 cm of rain on a city 4 km wide and 8 km long in a 2-h period. Part A How many metric tons (1 metricton = 103 kg) of water fell on the city? (1 cm3 of water has a mass of 1 gram = 10-3 kg.) Express your answer using o

Answer 1

Answer:

The mass of water in metric tonnes equals $32\times 10^{4}$ metric tonnes.

Step-by-step explanation:

To compute the mass of the rain water we intially need to compute the volume of the water that is collected in the city.

Since it is assumed that the city is flat we can obtain the volume of the rainwater as

$Volume=Area\times Height\\\\Volume=Length\times Width\times Height\\\\Volume=4\times 1000\times 8\times 1000\times 1.0\times 10^{-2}\\\\\therefore Volume =32\times 10^{4}m^{3}$

Now since it is given that the density of water is 1 gram per cubic centimeter thus we have

$1m^{3}Water=1000kg$

Thus the mass of the calculated volume of water becomes

$Mass_{water}=1000\times 32\times 10^{4}\\\\Mass=32\times 10^{7}kg$

Now since we know that 1 metric ton equals 1000 kg thus the total weight in metric tonnes equals

$Mass_{tonnes}=\frac{32\times 10^{7}}{10^{3}}\\\\Mass_{tonnes}=32\times 10^{4}tonnes$