(Old Final Exam Problem-A2011)
A right circular cone of height $h$ and base radius $r$ has total surface area $S$ consisting of its base area plus its side area, leading to the formula:
$S = \pi r^2 + \pi r \sqrt{r^2 + h^2}$
Suppose you start out with a cone of height 8 cm and base radius 6 cm, and you want to change the dimensions in such a way that the total surface area remains the same. Suppose you increase the height by 28/100. In this problem, use tangent line approximation
to estimate the new value of $r$ so that the new cone has the same total surface area.
The estimated value of $r = \boxed{}$