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 4000 km on a side and 28 km deep and the rock has an average mass density of 2950 kg/m3 . The continent is moving at the rate of about 4.6 cm/year. What is the mass of the continent? (answer in units of kg.)

A) 5.67×10^23 kg
B) 1.38×10^24 kg
C) 3.45×10^24 kg
D) 8.21×10^24 kg

Answer 1

The mass of the North American continent represented as a slab of rock can be approximated using the volume and mass density of rock. Upon calculating, the closest approximation to the actual mass is 3.45×10⁲⁴ kg (Option B).

Step-by-step explanation:

To calculate the mass of the North American continent based on its representation as a slab of rock, we use the formula for the mass of a rectangular prism, which is mass = density × volume. The volume of the continent is given by its dimensions, which are 4000 km on each side and 28 km deep. Since 1 km = 1000 m, the volume in cubic meters is (4000 × 1000) × (4000 × 1000) × (28 × 1000). With the average mass density of 2950 kg/m³, the mass (m) can be found as:

m = 2950 kg/m³ × 4000 km × 1000 m/km × 4000 km × 1000 m/km × 28 km × 1000 m/km

m = 2950 kg/m³ × 1.12 × 10ⁱ⁷ m³

m = 3.304 × 10⁲⁳ kg

The closest answer choice to this calculation is B) 3.45×10⁲⁴ kg, which can be considered an approximation of the actual mass calculated.