Twelve solid sphere of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

Given: A solid metallic cylinder of base diameter 2 cm and height 16 cm.

Twelve solid sphere of the same size are made by melting a solid metallic cylinder .

Let V₁ be the volume of the cylinder

Volume of the cylinder is given by: π × r² × h

∴ V₁ = π × 1² × 16 (diameter is 2cm, ∴ radius is 1cm)

Let V₂ be the volume of the each Sphere.

Volume of the Sphere is given by: × π × r³ (where r is the radius of the sphere)

∴ V₂ = × π × r³

Here,

V₁ = 12 × V₂

∴ π × 1² × 16 = 12 × × π × r³

⇒ r³ = = = 1cm

∴ r = ∛1 = 1 cm

∴ Diameter of the Sphere is 2 × r = 2 × 1 = 2cm