N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is:

Solution (By Examveda Team)

\[\begin{array}{*{20}{c}} {}&{{\text{Sphere}}}&{}&{{\text{Cylinder}}} \\ {{\text{Radius}} \to }&R&:&{3R} \\ {{\text{Height}} \to }& - &{}&{4R} \end{array}\]
$$\eqalign{ & N \times \frac{4}{3}\pi {R^3} = \pi {\left( {3R} \right)^2} \times 4R \cr & N \times \frac{4}{3}{R^3} = 3 \times 4{R^3} \cr & N = 27 \cr} $$