A cylindrical vessel with radius 6 cm and height 5 cm is to be made by melting a number of spherical metal balls of diameter 2 cm. The minimum number of balls needed is:

Given, radius of the cylindrical vessel = 6 cm

Height of the cylindrical vessel = 5 cm

Volume of the cylindrical vessel = $$\pi\ r^2h=\pi\ \left(6\right)^2\left(5\right)=180\pi\ $$

Diameter of the spherical metal ball = 2 cm

$$=$$>  Radius of the spherical metal ball = 1 cm

Volume of the spherical metal ball = $$\frac{4}{3}\pi\ r^3\ =\frac{4}{3}\pi\ \left(1\right)^3=\frac{4}{3}\pi\ $$

Let the number of spherical metal ball to be melted to make cylidrical vessel = $$n$$

$$=$$>  $$n\times\frac{4}{3}\pi=180\pi\ \ $$

$$=$$>  $$n=180\times\frac{3}{4}\ \ $$

$$=$$>  $$n=135$$

$$\therefore\ $$Number of spherical metal balls required to melt = 135

Hence, the correct answer is Option D