Using the density values of ocean floor crust and a mantle xenolith given in Question 2.1, what would be the density of material at 2900 km depth (where Earth’s core begins) if we could assume that density increases linearly with depth?

Data from question 2.1

(a) The mass of the Earth has been determined as 5.9737 × 10²⁴ kg. Calculate the
Earth’s bulk (i.e. mean) density. You should assume the Earth is a sphere with a
radius of 6371 km. Quote your answer to 3 significant figures.

(b) Examination of the composition of rocks comprising Earth’s continental crust
and ocean floor crust gives a bulk density of 2.7 × 10³ kg m⁻³ and 3.0 × 10³ kg m⁻³,
respectively, whilst that of the densest rocks (i.e. xenoliths brought up from
depths of up to 100 km) is about 3.5 × 10³ kg m⁻³. How do these densities compare
with Earth’s bulk density, and what does your result from (a) suggest about density
variation with depth?