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 ______.

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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 2 cm. Explanation: As we know, Volume of cylinder = $\pi$r2h Where r = base radius h = height of cylinder For given solid cylinder, Base diameter = 2 cm Base radius, r = 1 cm ...[As radius = $\frac{1}{2}$ diameter] Height, h = 16 cm Volume of cylinder, V = $\pi$(1)2(16) = 16$\pi$ cm3 Now, Let the radius of sphere be r Volume of sphere = $\frac{4}{2}$ pir^3 Where r = radius Volume of 12 spheres of radius r = 12($\frac{4}{3}$ pir^3) = 16 pir^3 Now, Volume of 12 spheres = Volume of cylinder ...[As volume remains same, when a metal body is melted and recast into another metal body] $\Rightarrow$ 16$\pi$r3 = 16$\pi$ $\Rightarrow$ r3 = 1 $\Rightarrow$ r = root(3)1 = 1 cm Diameter = 2r = 2 cm Hence, diameter of each sphere is 4 cm.

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