The height of a cone, a cylinder and a sphere are equal numerically. If the ratio of their radii is 1:3:5, then find the ratio of their volumes?

1:27:200

since in a sphere, height = diameter :- 

                             Cone             Cylinder           Sphere

Ratio of radius           1         :          3           :        5

Ratio of height           1        :          1           :        1 

                      ⇒ height of cone and cylinder = diameter of sphere

Ratio of volume     \(\frac{1}{3}\) \(\pi \)r₁²h₁  :   \(\pi \)r₂²h₂   :   \(\frac{4}{3}\) \(\pi \)r₃³

⇒  \(\frac{1}{3}\) \(\pi \)x² × \(\frac{5x}{2}\)  :   \(\pi \)(3x)² \(\frac{5x}{2}\)  :    \(\frac{4}{3}\) \(\pi \) 5x)² 

⇒ \(\frac{5}{6}\)  :   \(\frac{9 × 5}{2}\)   :   \(\frac{4}{3}\) × 125

= 1  :  27  :  200