Question

Explain how the core is only one-sixth of Earth's volume, yet it is onethird of Earth's mass.

Short answer

The core is denser due to iron and nickel, resulting in a larger mass despite smaller volume.

Step-by-step solution

Understanding Earth's Composition

The Earth is composed of three main layers: the crust, the mantle, and the core. The core is predominantly made up of iron and nickel, which are dense materials.

Volume and Density Relationship

The volume of an object depends on its density as well as its mass, expressed as \( V = \frac{M}{\rho} \), where \( V \) is volume, \( M \) is mass, and \( \rho \) is density. High-density materials will have a smaller volume for the same mass compared to low-density materials.

Calculating Earth's Core Volume

The core represents only one-sixth of Earth's volume which implies, based on geometry and volume calculations, that its structure occupies a smaller spatial region compared to the mantle and crust.

Evaluating Earth’s Core Mass Contribution

Despite its small volume, the core contains one-third of Earth's total mass primarily due to its high density compared to the other Earth layers. Iron and nickel, which are heavy elements, contribute significantly to the mass.

Conclusion

This results in the core having a disproportionately larger contribution to the Earth's mass than to its volume, making it one-third of the Earth’s mass while only being one-sixth of its volume.

Key concepts

Earth's Layers

The Earth is like a giant onion, but instead of layers of vegetable, it has layers of solid and molten rock. Each of these layers has distinct characteristics that contribute to Earth's overall structure. At the very surface lies the **crust**, which is the thinnest layer and is composed of a variety of elements primarily including silicates like granite and basalt. Beneath the crust is the **mantle**, which is much thicker and made up of silicate minerals rich in magnesium and iron. The mantle is semi-fluid, allowing for movement that drives plate tectonics.

The innermost **core** is composed primarily of iron and nickel. This dense inner core is split into two parts: a solid core and a liquid outer core. Despite its small volume, it is remarkably dense compared to the other layers, which results in the core having a significant impact on Earth's mass. This dense composition is the reason for many of Earth's magnetic properties, as the moving metal creates Earth's magnetic field.

The interplay of these layers, including their composition and density, has profound effects on geophysical processes like volcanism and earthquakes, fundamentally shaping the Earth we live on.

Density and Mass Relationship

Density is a measure of how much mass is contained in a given volume. Imagine packing a suitcase: density is like how tightly all your clothes are packed inside. Mathematically, density is represented as \( \rho = \frac{M}{V} \), where \( \rho \) is density, \( M \) is mass, and \( V \) is volume.

This concept plays a crucial role in understanding why the Earth's core has such a significant portion of Earth's mass. Despite its smaller volume, the dense materials like iron and nickel mean the core houses a large chunk of mass. In simpler terms:

• A dense layer (the core) will have a lot of mass packed into a tiny space versus a less dense layer (like the mantle or crust).
• If you compare an equal volume of each layer, the core will weigh more because of its higher density.

This relationship helps explain why the Earth’s core is one-third of the Earth's mass while only occupying one-sixth of its volume. The mass is packed more tightly within the core, making it a heavyweight in terms of Earth's total mass.

Volume Calculations

Calculating volume is essential for understanding the distribution of mass within the Earth. Volume is the amount of space something occupies and can be influenced by the object's shape. For Earth’s inner layers, like the core, advanced calculations consider sphere-like volumes because of Earth’s nearly spherical shape.

When talking numbers, the core's volume is determined via the formula for the volume of a sphere: \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius of the core. Since the radius of the core is much smaller than that of the mantle or the crust, it takes up a lesser proportion of total volume. The one-sixth figure comes from comparing the core's volume ratio to that of the whole Earth.

This mathematical approach helps visualize why such a dense region contributes less to the Earth’s total volume, emphasizing the concentration of mass due to density rather than sheer space occupied. Thus, thorough volume calculations reveal why this smaller space can account for so much weight, illuminating the dense nature of the materials within the core.