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Im getting a slightly different answer to the one that is needed for the following question:

2) A positive charge Q is distributed throughout a spherical volume of radius R in vacuum.

The charge density rho varies with the radius according to the linear law rho = a r. Show that the parameter a is Q/(pi R^4).

I started by saying that I'm looking at the position where r=R, i.e. at the surface itself. At this point the total charge Q must be present. Hence Q= rho x volume = a x r x volume, and as R=r Q= a x R x volume. Therefore Q = a x r x (4/3)pi R^3, which gives an a similar to the one required, but multiplied by 3/4.

Any ideas where I am going wrong?

Thanks