jmc

First, let us denote the radius of cylinder A (and height of cylinder B) as $r$, and the height of cylinder A (and radius of cylinder B) as $h$. Therefore, if the volume of cylinder A is double that of B, then: $\frac{\text{Volume of Cylinder A}}{\text{Volume of Cylinder B}}=\frac{r^2\cdot h}{h^2\cdot r}=\frac{r}{h}=2$. Therefore, normally the volume of Cylinder A is expressed as $\pi \cdot r^2\cdot h$, and plugging in $r=2h$, we see that the volume of Cylinder A $=4\pi \cdot h^3$, hence $N=\boxed{4}$.