Elliptically symmetric random variable

Question

Let $X$ is elliptically symmetric distributed random vector. Then $X$ can be expressed in the form $$X =^d \mu + R A U$$ where $R$ is a nonnegative random variabel and $U$ is uniformly distributed random vector in unit sphere, $U$ and $R$ are mutually independent. Is it true that $R =^d ||X||$ ? Where $||X||$ denote euclidean norm of $X$. I hope someone can help me. Thanks.