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math - Finding largest cylinder to be placed in a sphere of a given radius

Take both volumes, viz.: pi r^2 h to be < 4/3 pi a^3, to distinguish between radii of the 2 figures, let us call the radius of the sphere a

pi is divided out

r^2 h < 4/3 a^3

It is time to take the derivate in order to find the maximal r, but the 4/3 a^3 in case of differentiating on r, is a constant, and is lost in the derivative. With thus all useful info is lost. But I see no way to retain the constant in the derivative. Or is there a cleverer way? thank you


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