Question 1198591
Total surface area of a cone ={{{ pi*r*(r+sqrt(r^2+h^2))}}}

Lateral surface area of a cone = {{{ pi*r*sqrt(r^2+h^2)}}}

The total surface area of a right circular cone is {{{one}}} and {{{one-half}}} times the lateral area.
{{{one}}} and {{{one-half}}}=>{{{3/2}}}


 {{{pi*r*(r+sqrt(r^2+h^2))= (3/2)(pi*r*(sqrt(r^2+h^2)))}}}.........simplify

{{{r* sqrt(h^2 + r^2) = 2 r^2}}}.......if  {{{ h=6}}}

{{{r *sqrt(36 + r^2) = 2r^2}}}...........simplify

{{{sqrt(36 + r^2) = 2r}}}........square both sides

{{{36 + r^2 = 4r^2}}}

{{{36 = 4r^2-r^2 }}}

{{{3r^2 =36}}}

{{{r^2 =12}}}

{{{r=sqrt(12)}}}

{{{r}}}≈{{{3.464}}} inches