The total surface area of a cone is 770 cm² . If its slant height is four times the radius of the cone, the diameter of the cone is

Given, total surface area of cone $=770 c{m}^2$
Slant height $=4\times$radius of cone
l $=$4r
 $$\begin{gathered} \mathrm{\pi r}\left(\mathrm{l}+\mathrm{r}\right)=770 \\ \mathrm{\pi r}\left(4\mathrm{r}+\mathrm{r}\right)=770 \\ 5{\mathrm{\pi r}}^2=770 \\ 5\times \frac{22}{7}\times {\mathrm{r}}^2=770 \\ {\mathrm{r}}^2=\frac{770\times 7}{110} \\ {\mathrm{r}}^2=7\times 7 \\ \mathrm{r}=7 \end{gathered}$$
There fore Diameter of cone = 14 cm