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Mathematics

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

  1. 4 cm

  2. 3 cm

  3. 2 cm

  4. 6 cm

Mensuration

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Answer

Diameter of cylinder = 2 cm

Radius of cylinder (r) = 22\dfrac{2}{2} = 1 cm and height (h) = 16 cm.

Given, 12 spheres are formed from this cylinder.

∴ Volume of cylinder = 12 × Volume of each sphere.

Let radius of each sphere be R.

∴πr2h=12×43πR3⇒R3=3π(1)2×164π×12⇒R3=48π48π⇒R3=1⇒R=1 cm.\therefore πr^2h = 12 \times \dfrac{4}{3}πR^3 \\[1em] \Rightarrow R^3 = \dfrac{3π(1)^2 \times 16}{4π \times 12} \\[1em] \Rightarrow R^3 = \dfrac{48π}{48π} \\[1em] \Rightarrow R^3 = 1 \\[1em] \Rightarrow R = 1 \text{ cm}.

Diameter = 2 × Radius = 2 cm.

Hence, Option 3 is the correct option.

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