Charge Density Expression

Homework Statement

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. Write the expression of the charge density in the sphere?

Homework Equations

Charge density ρ=dQ/dV
Gauss's Law ∫EdA = E(4ϖr^2)

The Attempt at a Solution

If Q is uniform then ρ=Q/dV and the volume of a sphere is 4/3ϖr^3 then I think charge density would just be ρ=Q/(4/3ϖr^3).
This is suspiciously simple so I would just like external input on the problem. I have a feeling that I may need to use Gauss's Law somehow.

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Homework Statement

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. Write the expression of the charge density in the sphere?

Homework Equations

Charge density ρ=dQ/dV
Gauss's Law ∫EdA = E(4ϖr^2)

The Attempt at a Solution

If Q is uniform then ρ=Q/dV and the volume of a sphere is 4/3ϖr^3 then I think charge density would just be ρ=Q/(4/3ϖr^3).
This is suspiciously simple so I would just like external input on the problem. I have a feeling that I may need to use Gauss's Law somehow.
That's all there is to it. ##Q## could be anything uniformly distributed across volume ##V## and the density is, by definition, ##Q/V##.