The correct option is C 13cm
The ratio of the radius and height of a cone is 5:12.
rh=512. ...... (1)
The volume of the cone =314cm3
⟹ 13πr2h=314
⟹ r2h=300. ........ (2)
On solving equation (1) and (2), we get,
r=5 cm and h=12 cm.
Then, the slant height is l=√h2+r2
⟹ l=√122+52
⟹ l=13 cm.
Hence, option C is correct.