A solid metallic sphere of radius 6.3 cm is melted and recast into a right circular cone of height 25.2 cm. What is the ratio of the diameter of the base to the height of the cone?

Radius of sphere = $$R=6.3$$ cm

Let radius of cone = $$r$$ cm and height of cone = $$h=25.2$$ cm

Now, volume of cone = volume of sphere

=> $$\frac{1}{3}\pi r^2h=\frac{4}{3}\pi R^3$$

=> $$r^2\times25.2=4\times(6.3)^3$$

=> $$r^2=4\times\frac{6.3\times6.3\times6.3}{25.2}$$

=> $$r^2=(6.3)^2$$

=> $$r=6.3$$

$$\therefore$$ Ratio of diameter and height of cone = $$\frac{2r}{h}=\frac{12.6}{25.2}$$

= $$1:2$$

=> Ans - (C)