Q. 153.7( 3 Votes )
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)
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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