The ratio of the radius and height of a cone is 5 : 12. Its volume is 314 2/ 7 cm 3. Its slant height is?

Let radius = 5k, height = 12k
According to the question
= 1/3 x 22/7 x (5k)² x 12k = 2200/7
⇒ k = 1
∴ r = 5, h = 12
∴ Slant height (l) = √r² + h²
= √25 + 144
= √169
=13 cm