Finding the radius of frustum cone?

Question

I'm trying to understand how can i find the radius from the figure , the solution of the radius is given in the equation but I'm not getting how its derived

Answer 1

The radius increases linearly from $r_1$ at the top to $r_2$ at the bottom. The total increase in radius is $r_2-r_1$. So when you are $\frac{z}{h}$ of the way from the top to the bottom (as indicated in the figure), the radius has increased by $\frac{z}{h}$ times the total increase in radius, i.e., by $\frac{(r_2-r_1)}{h}z$. Adding this to the initial radius tells you that the radius is $r_1+\frac{(r_2-r_1)}{h}z$ at a distance $z$ from the top.