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 4500 km on a side and 32 km deep, and that the rock has an average mass density of 2950 kg/m^3. The continent is moving at the rate of about 4.2 cm/year. What is the mass of the continent?

a) 1.5 x 10^21 kg
b) 2.3 x 10^20 kg
c) 3.7 x 10^22 kg
d) 4.8 x 10^23 kg

Answer 1

By multiplying the continent's volume by its density, we determine that the mass of the North American continent is closest to 1.5 × 10^21 kg, which corresponds to answer choice (a).

Step-by-step explanation:

To find the mass of the North American continent based on the given dimensions and density, we can use the formula for mass: mass = volume × density. First, we calculate the volume by multiplying the continent's length, width, and depth. Then we multiply the volume by the density to get the mass.

So, volume = 4500 km × 4500 km × 32 km = 4500 × 10^3 m × 4500 × 10^3 m × 32 × 10^3 m = 6.48 × 10^17 m^3.

Next, mass = volume × density = 6.48 × 10^17 m^3 × 2950 kg/m^3 = 1.9116 × 10^21 kg. The closest answer choice to this calculated mass is (a) 1.5 × 10^21 kg, assuming the options given round the numbers accordingly.