The radius of a cone is 5cm and vertical height is 12 cm.

It is given that:

Radius of cone (r) = 5 cm

Height of the tent (h) = 12 cm

Slant Height of tent (l) = ?

Curved Surface Area (C. S. A) = ?

Now we know we that,

$I=r^{2}+h^{2}$

$\mathrm{l}^{2}=\mathrm{r}^{2}+\mathrm{h}^{2}$

$I^{2}=5^{2}+12^{2}$

$1^{2}=25+144$

⟹ l = 13 cm

Now,

C.S.A = πrl 

= 3.14 * 5 * 12

$=204.28 \mathrm{~cm}^{2}$

Therefore the curved surface area of the cone is $204.28 \mathrm{~cm}^{2}$