The World Geodetic System (the international standard used by GPS devices) models the Earth as an oblate spheroid described by the equation $$x^2/a^2+y^2/a^2+z^2/b^2=1$$
where a ≈ 6378.1370 km is the equatorial radius, and b ≈ 6356.7523 km is the polar radius. Use this information and a triple integral to calculate an estimate of the volume of the Earth.
The triple integral for the volume is
$$V=\int_{A(x,y)} \int_{-b\sqrt{1-x^2/a^2-y^2/a^2}}^{b\sqrt{1-x^2/a^2-y^2/a^2}}dzdydx$$ $$=2b\int_{A(x,y)} \sqrt{1-x^2/a^2-y^2/a^2}dydx$$
In polar coordinates,
$$V= 2b\int_0^{2\pi}\int_0^a \sqrt{1-r^2/a^2}rdrd\theta=\frac43\pi ba^2$$
which is about 1.083$\times 10^{12}$km$^3$.