What will be the Thickness of Gold? If

A ball of lead 4 cm in diameter is covered with gold. If the volume of the gold and lead are equal, Then the thickness of gold

  1. 5.038 cm
  2. 5.190 cm
  3. 1.038 cm
  4. 0.519 cm
Tahir Lecturer Asked on 17th July 2015 in No Category.
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  • 1 Answer(s)

    Answer: (4) 0.519 cm
    Explanation:-
    The volume of lead = the volume of gold
    Diameter = 4 cm
    Let be the total diameter is D  & d = 4 cm
    According to the question,
    D  = the thickness of the gold x 2 + d                       ………………………………. (1)
    Then,
    pie x d3/6 = pie (D3– d3)/6
    d3 = D3 – d3
    d3+ d3 = D3
    2d3 = D3
    D3 = 2 (4)3
    D3  = 2 x 64
    D3 = 128
    D = 5.038   (cube root of both side)
    Put the value of D in equation (1)
    5.038 = 2 x thickness of the gold + 4
    thickness of the gold = (5.038 – 4)/2
    = 1.038/2
    = .519 cm
    Hence, the answer is (4) .519 cm

    Anurag Mishra Professor Answered on 18th July 2015.
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