List of top Atmospheric Science Questions on Fourier series

The equation of a sphere is $3x^{2}+3y^{2}+3z^{2}+12x+18y+24z+30=0.$ The centre and radius of sphere, respectively, are:
Let \( g(x) = x^2 \), \( -\pi \le x \le \pi \). The coefficient of \( \cos(3x) \) in the Fourier series expansion of \(g(x)\) is: