Q. 153.7( 3 Votes )

# The number of sol

Answer :

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 × r^{2} × h (here r is radius and h is height)

Volume of the Solid Sphere is: × π × r^{3} (here r is the radius of the Sphere)

Let v_{1} be the volume of given Cylinder

∴ v_{1} = π × 2^{2} × 45 cm^{3} (4cm is diameter, ∴ 2cm is the radius of cylinder)

Let v_{2} be the volume of Solid Sphere.

V_{2} = × π × 3^{3} cm^{3} (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.

∴ v_{1}=n × v_{2} (volume of n Spheres = volume of Cylinder)

That is,

π × 2^{2} × 45 =n × × π × 3^{3}

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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