Three spherical balls of radius 2 cm, 4 cm and 6 cm are melted to form a new spherical ball. In this process there is a loss of 25% of the material. What is the radius (in cm) of the new ball?

Let $$\ r_{1} = 2cm,\ r_{2} = 4cm,\ r_{3} = 6cm$$

There is a loss of 25% of the material, volume of the remaining spherical ball is given by,

$$\frac{3}{4}$$ x $$\frac{4}{3} \pi ((r_{1})^{3} + (r_{2})^{3} + (r_{3})^{3})$$

$$\pi (2^{3} + 4^{3} + 6^{3})$$ = $$\pi (8 + 64 + 216)=288\pi$$

Radius of the new ball is given by,

$$\frac{4}{3} \pi r^{3}$$ = $$288\pi$$ (or) $$r^{3} = 216$$ (or) $$r = 6cm$$

Hence, option A is the correct answer.