Presumably, both δ and ρ represent density of some object. Considering the context, ρ is likely a function of 3 variables, ρ = ρ(x, y, z). Then the mass of the sphere with the prescribed density δ(x, y, z) = k ρ(x, y, z) is
[tex]\displaystyle \iiint_B k \rho(x,y,z) \, dx\, dy\, dz[/tex]
where B is the set
[tex]B = \left\{(x,y,z) ~ : ~ x^2+y^2+z^2 \le 7^2\right\}[/tex]
If you have all the details at hand, you can compute the integral by converting to spherical coordinates, substituting
[tex]\begin{cases}x = u \cos(v) \sin(w) \\ y = u \sin(v) \sin(w) \\ z = u \cos(w)\end{cases} \text{ and } dx\,dy\,dz = u^2 \sin(w) \, du \, dv \, dw[/tex]
The integral then transforms to
[tex]\displaystyle k \int_0^{2\pi} \int_0^\pi \int_0^7 \rho(u\cos(v)\sin(w),u\sin(v)\sin(w),u\cos(w)) \, u^2 \sin(w) \, du \, dw \, dv[/tex]
Without any additional information, there's not much more to say...
