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in Surface Areas And Volumes by (48.8k points)
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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

1 Answer

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Best answer

A. 4 cm

As we know,

Volume of cylinder = πr2h

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 cm3

Now,

Let the radius of sphere be r

Volume of sphere = 4/3πr3 

where r = radius

Volume of 12 spheres of radius r = 12 (4/3πr3) = 16πr3

Now,

Volume of 12 spheres = volume of cylinder

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

⇒ 16πr3 = 16π

⇒ r3 = 1

⇒ r = ∛1 = 1 cm

Diameter = 2r = 2 cm

Hence, diameter of each sphere is 4 cm.

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