Given, the ratio of the base radius and the height of the right circular cone =3:5.
Suppose the base radius and the height of the right circular cone are 3x m and 5x m, respectively.
∴ Volume of the cone =13πr2h =13π(3x)2×5x.
According to question:
Volume of the cone=120πm3
∴13π×9x2×5x=120π
x3=120×39×5
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 l=√r2+h2
=√(6)2+(10)2
=√36+100
=√136=2√34 m.
Hence, option D is correct.