Suppose the base radius and the height of the right circular cone are 3x m and 5x m respectively. ∴ Volume of the cone =
1
3
πr2h =
1
3
π(3x)2×5x cu m Now,
1
3
π×9x2×5x = 120π ⇒ x3 =
120×3
9×5
⇒ x3 = 8 ⇒ x3 = (2)3 ⇒ x = 2 m ∴ The radius and the height of the cone will be 3 × 2 = 6 m and 5 × 2 = 10 m respectively. ∴ Slant height of the cone = √r2+h2 = √(6)2+(10)2 = √36+100 = √136 = 2√34 m.