Question

Assuming the Earth to be an ideal sphere, the volume % of the core relative to the total volume of the Earth is .......... (answer in one decimal place).

Hint:

For volume calculations, use the formula for the volume of a sphere, and compare the volume of different layers (core, mantle, crust) to find their relative volumes.

Answer 1

Correct Answer: 14 - 18

Step 1: Understand the problem setup. 
The Earth can be modeled as a sphere. The core is the inner part of the Earth, and the rest of the Earth is made up of the mantle and crust. To solve this, we need to use the formula for the volume of a sphere: \[ V = \frac{4}{3} \pi r^3 \] The core radius is roughly 3,500 km, and the total Earth radius is around 6,371 km. We need to calculate the volume of the core and the total volume of the Earth.

Step 2: Calculate the volume of the Earth and the core. 
The total volume of the Earth: \[ V_{\text{Earth}} = \frac{4}{3} \pi (6371)^3 \approx 1.08321 \times 10^{12} \, \text{km}^3 \] The volume of the core: \[ V_{\text{Core}} = \frac{4}{3} \pi (3500)^3 \approx 1.7764 \times 10^{11} \, \text{km}^3 \]

Step 3: Calculate the volume percentage. 
The volume percentage of the core relative to the total volume of the Earth is: \[ \text{Volume \% of Core} = \left( \frac{V_{\text{Core}}}{V_{\text{Earth}}} \right) \times 100 = \left( \frac{1.7764 \times 10^{11}}{1.08321 \times 10^{12}} \right) \times 100 \approx 16.4\% \]

Step 4: Conclusion. 
The volume percentage of the core relative to the total volume of the Earth is 16.4%.