Find The Height Of The Cone With Diameter Of The Base

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

  1. 2 cm
  2.  3 cm
  3.  4 cm
  4.  6 cm

 

Anurag Mishra Professor Asked on 19th July 2015 in Maths.
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  • 1 Answer(s)

    Answer: (2) 3 cm
    Explanation:-
    The diameter of solid metallic ball = 6 cm    (Given)
    Then, the radius of this ball = 6 /2 = 3 cm
    Formula-
    The volume of solid metallic ball = 4 x pai x r3/3
    Where, r = radius of the ball
    Now, the volume of spherical ball = 4 x 22 x 33/3 x 7 = 88 x 9/7 = 792/7 cm3The volume of spherical ball = the volume of cone            (According to the question)
    Formula-
    The volume of cone = Pai x r2 x h/3
    Where, r = radius of the cone & h = height of the cone.
    The diameter of the cone = 12 cm      (Given)
    Then, the radius of the cone (r)  = 12/2 = 6 cm
    Now, the volume of the cone = 22 x (6)2 x h/3 x 7 = 792/7
    22 x 6 x 2 x h/7 = 4 x 22 x 3 x 3/7
    h = 3 cm
    Hence, the height of the cone is (2) 3 cm.

    Anurag Mishra Professor Answered on 19th July 2015.
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