Indiana Jones is in a temple searching for artifacts. He finds a gold sphere with a radius of 2 cm sitting on a pressure sensitive plate. To

Question

Indiana Jones is in a temple searching for artifacts. He finds a gold sphere with a radius of 2 cm sitting on a pressure sensitive plate. To avoid triggering the pressure plate, he must replace the gold with something of equal mass. The density of gold is 19.3.103 kg/m3, and the volume of a sphere is V = 4/3 Ar3. Indy has a bag of sand with a density of 1,602 kg/m3.
(A) What volume of sand must he replace the gold sphere with? If the sand was a sphere, what radius would it have?

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Doris 3 years 2021-08-17T15:45:58+00:00 1 Answers 7 views 0

Answers ( )

  1. Farah
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    2021-08-17T15:46:58+00:00
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    Answer:

    Volume of Sand = 0.4 m³

    Radius of Sand Sphere = 0.46 m

    Explanation:

    First we need to find the volume of gold sphere:

    Vg = (4/3)πr³

    where,

    Vg = Volume of gold sphere = ?

    r = radius of gold sphere = 2 cm = 0.02 m

    Therefore,

    Vg = (4/3)π(0.2 m)³

    Vg = 0.0335 m³

    Now, we find mass of the gold:

    ρg = mg/Vg

    where,

    ρg = density of gold = 19300 kg/m³

    mg = mass of gold = ?

    Vg = Volume of gold sphere = 0.0335 m³

    Therefore,

    mg = (19300 kg/m³)(0.0335 m³)

    mg = 646.75 kg

    Now, the volume of sand required for equivalent mass of gold, will be given by:

    ρs = mg/Vs

    where,

    ρs = density of sand = 1602 kg/m³

    mg = mass of gold = 646.75 kg

    Vs = Volume of sand = ?

    Therefore,

    1602 kg/m³ = 646.75 kg/Vs

    Vs = (646.75 kg)/(1602 kg/m³)

    Vs = 0.4 m³

    Now, for the radius of sand sphere to give a volume of 0.4 m³, can be determined from the formula:

    Vs = (4/3)πr³

    0.4 m³ = (4/3)πr³

    r³ = 3(0.4 m³)/4π

    r³ = 0.095 m³

    r = ∛(0.095 m³)

    r = 0.46 m

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