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 metrict

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Alona

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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 metrict

on = 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

Mathematics

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-03-06T13:26:32+03:00

Answer:

The amount of water collected in metric tonnes is $32\times 10^{4}$ metric tonnes.

Step-by-step explanation:

First, we need to calculate the volume of rainwater gathered in the city.

Assuming the city is level, we can determine the volume of the rainfall using

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

Given that the water density is 1 gram per cubic centimeter, we can deduce

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

This means the mass of the computed water volume is

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

Since we also know 1 metric ton is equivalent to 1000 kg, the total mass in metric tonnes is

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