The International Avogadro Coordination project created the world's most perfect sphere using Silicon in its crystalline form. The diameter of the sphere is $9.4 \,cm$ with an uncertainty of $0.2 \,nm$. The atoms in the crystals are packed in cubes of side $a$. The side is measured with a relative error of $2 \times 10^{-9}$, and each cube has $8$ atoms in it. Then, the relative error in the mass of the sphere is closest to (assume molar mass of Silicon and Avogadro's number to be known precisely)

  • [KVPY 2021]
  • A

    $6.4 \times 10^{-9}$

  • B

    $4.0 \times 10^{-10}$

  • C

    $1.2 \times 10^{-8}$

  • D

    $5.0 \times 10^{-8}$

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