A right circular cone of heighthand base radiusrhas total surface areaSconsisting of its base area plus its side area, leading to the formula:

S=r²+r*root 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 by60/100. In this problem, use tangent line approximation to estimate the new value ofrso that the new cone has the same total surface area.

The estimated value ofr=