Correct Answer: 32 : 25

Solution : The volume of the cone = $\frac{1}{3}$πr ² h, where r is the radius and h is the height.
Let the radius of one cone be 5r and 6r.
height is h ₁ and h ₂
⇒  $\frac{1}{3}$(π × 25r × h ₁ ) : $\frac{1}{3}$(π × 36r × h ₂ ) = 25h ₁ : 36h ₂
According to the question,
25h ₁ : 36h ₂ = 8 : 9
⇒ h ₁ : h ₂ = (8 × 36) : (25 × 9)
$\therefore$ h ₁ : h ₂ = 32 : 25
Hence, the correct answer is 32 : 25.