# A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Volume of the sphere $$= \ \frac{4}{3} \pi r^3 \ = \ \frac{4}{3} \ × \ \pi \ × \ (4.2)^3$$ cm3

If h is the height of a cylinder of radius 6 cm. Then its volume $$= \ \pi (6)^2 h \ = \ 36\pi h$$ cm3

$$\therefore$$ The volume of metal in the form of sphere and cylinder remains the same , we have

$$\Rightarrow 36 \pi h \ = \ \frac{4}{3} \ × \ \pi \ × \ (4.2)^3$$

$$\Rightarrow \ h \ = \ \frac{1}{36} \ × \ \frac{4}{3} \ × \ (4.2)^3$$

$$\Rightarrow \ h \ = \ 2.744$$ cm