The total surface area of a cone is 770${\text{cm}}^{\text{2}}$  . If its slant height is four times the radius of the cone, the diameter of the cone is

Given, total surface area of cone $=770{\text{cm}}^{\text{2}}$

Slant height $=4\times$ radius of cone

$l=4r$

$\pi r\left(l+r\right)=770$

$\pi r\left(4r+r\right)=770$

$5\pi r^2=770$

$5\times \frac{22}{7}\times r^2=770$

$r^2=\frac{770\times 7}{110}$

$r^2=7\times 7$

$r=7$

$\therefore$ Diameter of cone $=14\text{cm}$