# What's the simplest way to determine the mass of a sphere from a plot of its density varying in r?

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Answered: Torsten on 28 Nov 2022
Hey there,
So, within the context of a spherical body, I've got a plot of density varying in r which is generated through PDE solver. What would the neatest way of calculating the sphere's mass, based on said density plot, be?
Much appreciated.
##### 2 CommentsShowHide 1 older comment
And that would require curve fitting?

Torsten on 28 Nov 2022
If r and rho are column vectors where r is ordered as r(1) < r(2) < ... < r(n) and rho is the density at position r, an approximation for the mass m of the sphere is
m = trapz(r,4*pi*r.^2.*rho)

William Rose on 28 Nov 2022
I agree with @David Hill, except you want to multiply the density at each value of r by 4*pi*r^2*dr, then add them up, i.e. integrate. Because 4*pi*r^2*dr is the volume of each shell.

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