Q. 124.2( 10 Votes )

# Twelve solid spheres 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

A. 4 cm

B. 3 cm

C. 2 cm

D. 6 cm

Answer :

As we know,

Volume of cylinder = πr^{2}h

where r = base radius

h = height of cylinder

For Given Solid cylinder,

Base diameter = 2 cm

Base radius, r = 1 cm [as radius = 1/2 diameter]

Height, h = 16 cm

Volume of cylinder, V = π(1)^{2}(16) = 16π cm^{3}

Now,

Let the radius of sphere be r

Volume of sphere

where r = radius

Volume of 12 spheres of radius r =

Now,

Volume of 12 spheres = volume of cylinder

[As volume remains same, when a metal body is melted and recast into another metal body]

⇒ 16πr^{3} = 16π

⇒ r^{3} = 1

⇒ r = ∛1 = 1 cm

Diameter = 2r = 2 cm

Hence, diameter of each sphere is 4 cm.

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