a. A mass of 480,000 metric tonnes of water fell on the city.
b. The volume of water in is [tex]1.27\: × \:{10}^{8}\:gallons[/tex]
[tex]\\[/tex]
Explanation:
Given:
Depth = 1 cm = 0.01 m
Area = 6 km × 8 km = 6000 m × 8000 m
Density of water = 1000 kg/m³
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Conversion factors:
1 metric tonne = 1000 kg
1 gal = 3.785 L
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Required:
a. Metric tons of water that fell on the city
b. Volume of water in gallons
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Equation
V = Ad
where: V - volume
A - area
d - depth
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[tex]ρ \:=\: \frac{m}{v}[/tex]
where: ρ - density
m - mass
v - volume
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Solution:
a. Metric tons of water that fell on the city
Solve for volume in m
V = Ad
V = (6000 m × 8000 m)(0.01 m)
V = 480,000 m³
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Solve for mass
[tex]ρ \:=\: \frac{m}{v}[/tex]
[tex]1000 \:kg/m³\:=\:\frac{m}{480,000\:m³}[/tex]
[tex]m\:=\:(1000\:kg/m³)(480,000\:m³)[/tex]
[tex]m\:=\:(1000\:kg/m³)(480,000\:m³)[/tex]
[tex]m\:=\:(1000\:kg/m³)(480,000\:m³)[/tex]
[tex]m\:=\:4.8\:×\:{10}^{8}\:kg[/tex]
[tex]\\[/tex]
Convert to Metric tonnes
[tex]m\:=\:4.8\:×\:{10}^{8}\:kg\:×\frac{1\:metric\:ton}{1000\:kg}[/tex]
[tex]m\:=\:4.8\:×\:{10}^{5}\:metric\:tonnes[/tex]
or m = 480,000 metric tonnes
[tex]\\[/tex]
b. Volume of water in gallons
[tex]=\:480,000\:m³\:×\frac{1000\:L}{1\:m³}\:×\frac{1\:gal}{3.785\:L}[/tex]
[tex]=\:126,816,380.4\: gal[/tex]
[tex]or\: 1.27 \:× \:{10}^{8}\:gallons[/tex]
[tex]\\[/tex]
Final Answer:
a. A mass of 480,000 metric tonnes of water fell on the city.
b. The volume of water in is [tex]1.27\: × \:{10}^{8}\:gallons[/tex]
[tex]\\[/tex]
[tex]\\[/tex]
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