Great question! Scientists know about the interior through observations of Earth's gravity, seismic waves, electromagnetic field, and chondrites, a type of meteorite which formed at the same time as Earth.

Isaac Newton described the laws of gravitation between two objects as dependent on their masses and the distance between them. By observing the gravitational strength of planets, he determined that Earth's interior must be much denser than the rocks at Earth's surface. This was supported when the first numerical density was determined by Henry Cavendish in 1798.

Seismic waves provide more focused details of the structure of Earth's interior. Earthquakes are caused by the rupturing of cracks deep underground, which creates elastic waves that propagate away from the rupture. These waves are either compressional (P-waves; the fastest, primary wave) or shear (S-waves; the slower, secondary waves). As the waves travel through Earth, they are refracted, or bent (like light refracted through a prism), when they pass through different types of material. The speed of the waves depends on the density of that material. Therefore, seismic waves tell us that density increases with depth and that Earth is composed of several layers. Earth's layers are:

1) a brittle outer layer ranging in thickness from 5-10 km under the oceans and 25-70 km under continents, with a complex structure;

2) a dense solid (known to be solid because both S- and P-waves travel through it) mantle extending to a depth of 2890 km;

and 3) an extremely dense core, that must have a liquid outer portion (based on lack of S-waves and fact that S-waves cannot travel through liquid) and solid inner portion (based on presence of both S- and P-waves).

To understand what Earth is made of, scientists observe rocks that are brought up from Earth's deep crust and mantle through geologic processes (like volcanoes and the uplift of mountains) and through laboratory experiments simulating Earth's interior. Then the composition of rocks from Earth's surface and mantle are compared to the composition of chondrites, because scientists think that these meteorites were formed from the same material that formed Earth. The missing components from chondrites can be used as evidence for the composition of Earth's core. Earth's magnetic field further supports that Earth's core is mostly made up of iron and that the outer core is liquid. The composition of Earth's layers supports the density determined by seismic waves.

Therefore, scientists know that Earth's density ranges from ~2.2 g/cm³ in silicate rocks at Earth's surface to 13.1 g/cm³ in iron at Earth's center. And yes, it makes sense.

The Earth has a solid rocky mantle with a density of about 2.9 grams per cubic centimeter surrounding a molten outer core of metal, which in turn surrounds a solid inner metal core. The total density of the Earth is about 5.7 grams per cubic centimeter, so average that out to get the density of the metal core.

We know about the mantle and core because of the way that earthquake waves propagate through them: waves change direction as they move through media with different properties, in this case different density and temperature, just as light changes direction as it moves through a prism or crystal ball. We know the Earth's total density because we know its gravity.

There is also a thin rocky crust over the mantle that has a density that ranges from about 2.6 grams per cubic centimeter (continents) to 2.8 grams per cubic centimeter (ocean floors). This crust is so thin that its contribution to the Earth's total mass and density is almost negligible, however. Then there are the oceans themselves, which have even less mass, and the atmosphere, which has less mass yet.

I don't know what you mean by "why is this reasonable?". Each planet has its own characteristics. Venus has a much thicker crust than Earth does but may have a partially molten mantle underneath. Mars and Mercury are solid all of the way to the center, with no molten outer core. Venus has a thicker atmosphere, more comparable to Earth's oceans. Mars has a much thinner atmosphere, and Mercury has no appreciable atmosphere. Jupiter, Saturn, Uranus, and Neptune are all giant balls of gas where most of the planets' mass is atmosphere, completely the opposite of the Earth.