Question

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= π r2 + π r r2+h2 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 19/100. 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 =