Find the Diameter of Each Sphere ?

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. 2cm
  2. 3 cm
  3. 4 cm
  4. 6 cm
Anurag Mishra Professor Asked on 8th October 2015 in Maths.
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  • 1 Answer(s)

    Answer: (1) 2 cm

    Explanation:-
    Formula-
    Volume of the cylinder V = Pai x r2 x h
    Where, r = radius, h = height

    Then, V = pai x 1 x 16
    V = 16 pai
    divide by 12,
    Then, the volume of a small cylinder = 16 pai/12
    = 4 pai /3

    Formula-
    Volume of sphere = 4 pai x (d/2)3
    radius = diameter/2

    Then, volume of sphere = 4 pai (d/2)3/3
    4 pai/3 = 4 pai (d/2)3/3

    1 = (d/2)3
    Cube root on both side,
    1 = d/2
    by cross multiplication,
    d = 2 cm

    Then, the diameter of the sphere is 2 cm.

    Hence, the answer is  (1) 2 cm.

    Anurag Mishra Professor Answered on 11th October 2015.
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