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.

Radius of metallic sphere (r₁) = 4.2 cm, radius of cylinder (r₂) = 4.2 cm
Let, the height of cylinder = h
According to question, volume of sphere = Volume of cylinder
⇒ 4/3πr₁³ = πr₂²h ⇒ 4/3π(4.2)³ = π(6)²h
⇒ h = 4/3 × (4.2 × 4.2 × 4.2/36) = 1.4 × 1.4 × 1.4 = 2.74 cm
Hence, the height of cylinder is 2.74 cm.