# 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, isA. 2B. 4C. 5D. 6

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.

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