A solid sphere of radius 9 cm is melted to form a sphere of radius 6 cm and a right circular cylinder of same radius. The height of the cylinder so formed is ?

Radius of original sphere = $$R=9$$ cm

Radius of new sphere and cylinder = $$r=6$$ cm

Let the height of cylinder = $$h$$ cm

Volume of original sphere = Volume of new sphere + Volume of new cylinder

=> $$\frac{4}{3} \pi R^3=(\frac{4}{3} \pi r^3)+(\pi r^2 h)$$

=> $$\frac{4}{3} \times (9)^3=(\frac{4}{3} \times 6^3)+(6^2 \times h)$$

=> $$972=288+36h$$

=> $$36h=972-288=684$$

=> $$h=\frac{684}{36}=19$$ cm

=> Ans - (A)