\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The area bounded by the line \(y=x\) and the x-axis is revolved around the x-axis to form a cone.
  1. Find the volume of the cone generated if the region is from \(x=0\) to \(x=2\).
  2. Find a general formula for the volume of a cone with height \(h\) and radius \(r\) by revolving the line \(y=\frac{r}{h}x\) from \(x=0\) to \(x=h\).

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