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:

Solution

As a metallic sphere is melted and recast into the shape of a cylinder, their volume must be the same. Volume of the sphere = Volume of the cylinder Let us find the volume of the sphere and cylinder by using formulae; Volume of the sphere = 4/3πr³ where r is the radius of the sphere Volume of the cylinder = πr²h where r and h are radius and height of the cylinder respectively Radius of the sphere, r₁ = 4.2 cm Radius of the cylinder, r₂ = 6 cm Let the height of the cylinder be h. Volume of sphere = Volume of cylinder 4/3πr₁³ = πr₂²h (4/3)r₁³ = r₂²h h = 4r₁³ / 3r₂² = (4 × 4.2 cm × 4.2 cm × 4.2 cm) / (3 × 6 cm × 6 cm) = 2.744 cm Hence, the height of the cylinder so formed will be 2.744 cm.