I'm working on a problem involving a four-dimensional cone defined as follows: $C = \left\{\left(x,y,z,t\right)| (x,y,z) \in (1 - \frac{t}{12})B,0 \leq t \leq 12\right\}$ where the base $B$ is described by $x^2 + (y - 1)^2 + z^2 \leq 1$. I'm tasked with finding the volume (measure) of $\mu(C)$. I understand that the base $B$ is a three-dimensional ball centered at $(0,1,0)$ with a radius of 1. However, I'm unsure how to approach calculating the volume of this four-dimensional cone based on this information.
Could someone please provide guidance on how to compute the volume of this four-dimensional cone? Any step-by-step approach or insights into higher-dimensional geometry would be greatly appreciated!