Question

The current theory of the structure of the Earth, called plate tectonics, tells us that the continents are in constant motion. Assume that the North American continent can be represented by a slab of rock 4350 km on a side and 36 km deep, and that the rock has an average mass density of 2760 kg/m^3. The continent is moving at the rate of about 1.8 cm/year. What is the mass of the continent?

a) 1.9 x 10^19 kg
b) 1.2 x 10^22 kg
c) 2.5 x 10^20 kg
d) 4.8 x 10^21 kg

Answer 1

The mass of the North American continent is approximately 2.3 × 10^24 kg.

Step-by-step explanation:

To find the mass of the North American continent, we can use the formula:

Mass = Volume × Density

The volume of the continent can be calculated as:

Volume = (length × width × depth)

Substituting the given values:

Volume = (4350 km × 4350 km × 36 km)

Converting to meters:

Volume = (4350 × 10^3 m × 4350 × 10^3 m × 36 × 10^3 m)

Calculating:

Volume = 8.3316 × 10^20 m^3

Now, substituting the volume and density values into the mass formula:

Mass = (8.3316 × 10^20 m^3 × 2760 kg/m^3)

Calculating:

Mass = 2.2961 × 10^24 kg

Therefore, the mass of the North American continent is approximately 2.3 × 10^24 kg. This corresponds to option d) 4.8 x 10^21 kg.