A metallic sphere of radius 4.2 cms. is melted and recast into the shape of a cylinder of radius 6 cms. Height of the resultant cylinder would be:

If a sphere is recast into a cylinder, then its volume remains same
$$\dfrac{4}{3}\pi a^3 = \pi b^2 h$$ where a = radius of sphere = 4.2 cm and b = radius of cylinder = 6 cm

=> $$\dfrac{4}{3} \times \dfrac{42}{10}\times \dfrac{42}{10}\times \dfrac{42}{10} = 6\times6\times h$$

=> $$h = \dfrac{7\times7\times7}{5\times5\times5} = \dfrac{343}{125}$$

Therefore, $$h = 2.74 cm$$
Height of the cylinder = 2.74 cm.