Question 1085023
let r = the radius of the cone
then
{{{2/3}}}r = the height of the cone
:
Area formula A = {{{pi*r*sqrt(r^2+h^2)}}}
{{{pi*r*sqrt(r^2+((2/3)r)^2)}}} = 416.27
{{{pi*r*sqrt(r^2+(4/9)r^2)}}} = 416.27
{{{pi*r*sqrt((13/9)r^2)}}} = 416.27
extract the squares
{{{((pi*r^2)/3)*sqrt(13)}}} = 416.27
multiply both sides by 3
{{{pi*r^2*sqrt(13)}}} = 1248.81
divide both sides by the sq root of 13
{{{pi*r^2 = 346.3576}}}
divide both sides by pi
r^2 = 110.25
r = {{{sqrt(110.25)}}}
r = 10.5 cm is the radius of the cone