The number of solid sphere, each of diameter 6 cm, that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is

Given: Diameter of the Solid Sphere is: 6 cm

Height of the Cylinder is: 45cm

Diameter of the Cylinder is: 4cm

Volume of Solid Cylinder is: π × r² × h (here r is radius and h is height)

Volume of the Solid Sphere is: × π × r³ (here r is the radius of the Sphere)

Let v₁ be the volume of given Cylinder

∴ v₁ = π × 2² × 45 cm³ (4cm is diameter, ∴ 2cm is the radius of cylinder)

Let v₂ be the volume of Solid Sphere.

V₂ = × π × 3³ cm³ (6cm is the diameter, ∴ 3cm is the radius of the Sphere)

We know that when a object is moulded from one shape to other its volume does not change.

Let n be the number of Solid Sphere of diameter 6cm required.

∴ v₁=n × v₂ (volume of n Spheres = volume of Cylinder)

That is,

π × 2² × 45 =n × × π × 3³

n = = = = 5

That is 5 Solid Spheres of diameter 6 cm can be formed by the Solid Cylinder of height 45 cm and diameter 4 cm.