Find the Radius of the Hemisphere

A hemisphere of iron is melted and recast in the shape of a right circular cylinder of diameter 18 cm and height 162 cm. The radius of the hemisphere is

  1. 27 cm
  2. 9 cm
  3. 6 cm
  4. 12 cm
Abdul Salam Newbie Asked on 5th September 2015 in Maths.
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  • 1 Answer(s)

    Answer:  (1) 27 cm

    Explanation:-
    Given-
    Diameter of the cylinder = 18 cm
    Then, the radius of the cylinder = 18/2 = 9 cm
    Then height of the cylinder = 162 cm

    Formula-
    The volume of the cylinder = Pai x r2 h
    The volume of the cylinder = Pai x (9)2 x 162
    The volume of the hemisphere = 2 Pai x r3/3

    According to the question,
    Pai x (9)2 x 162 = 2Pai x r3/3
    9 x 9 x 9 x 18  = 2 x r3/3
    9 x 9 x 9 x 9 x 3 = r3
    r3 = 93 x 33
    r  = 9 x 3
    r = 27

    Then, the radius of the hemisphere is 27 cm
    Hence, the answer is (1) 27 cm.

    Anurag Mishra Professor Answered on 5th September 2015.
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