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Assuming 70% of Earth's surface is covered in water at an average depth of 2.3 mi, estimate the mass of the water on Earth in Kilograms.

Sagot :

starrynightsky

5.98E24 kg, and rounded I would not be able to determine, since it is a very large and complex equation.

The mass of the water on Earth in Kilograms with the given parameters is;

Mass = 97.335 × 10¹⁹ kg

We are given;

Average depth of water; h = 2.3 miles = 2701.49 m

Now, radius of earth is; r = 6400000 m

Also, density of water is; ρ = 1000 kg/m³

Since the earth is spherical, then surface Area is;

A = 4πr²

Thus; A = 4π × 6400000²

A = 16.384π × 10¹³ m²

Now, formula for volume is;

V = Ah

Thus; V = 16.384π × 10¹³  × 2701.49

V = 139.05 × 10¹⁶ m³

We are told the earth is 70% Water.

Thus, water volume = 0.7 × 139.05 × 10¹⁶

water volume = 97.335 × 10¹⁶ m³

Formula for mass from density and volume is;

mass = density × water volume

Thus;

mass = 1000 × 97.335 × 10¹⁶

Mass = 97.335 × 10¹⁹ kg

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