Answer :
Complete question is;
In the movie, "Raiders of the Lost Ark", Indiana Jones takes a gold idol from a cave. The statue is resting on a table which is rigged with a weight sensor. The weight sensor can detect when the weight is removed and will set off a series of unfortunate accidents. To prevent this from happening, Indiana replaces the gold idol with a bag of sand. The volume of the gold idol is approximately 1.0 L. The density of gold is 19.3 g/mL and the density of sand is 2.3 g/mL.
A) Assuming the idol is pure gold, what volume would the bag of sand have to be in order to weigh exactly the same as the idol and not set off the boo by-traps?
B) Let’s assume that Indiana is successful in removing the idol and returning with it to his laboratory. He decides to determine if it is really pure gold. He weighs the idol and measures the volume by a water displacement method. The results are: mass = 16.5 kg and volume of water displaced = 954 mL. Is the idol made of pure gold? Explain your answer based on the experimental results.
Answer:
A) Volume of sand = 8.391 L
B) The idol is not made of pure Gold.
Explanation:
A) We are given:
volume of the gold idol = 1 L = 1000 mL
Density of gold = 19.3 g/mL
Density of sand = 2.3 g/mL
So; mass of gold is gotten from the equation;
Density = mass/volume
Mass = density × volume
Mass of gold = 19.3 × 1000 = 19300 g
Now, we want to find what volume would the bag of sand have to be in order to weigh exactly the same as the idol.
Thus, volume of sand = 19300g/23 g/mL = 8391 mL or 8.391 L
B) We are now told the gold idol has;
mass = 16.5 kg = 16500 g
volume of water displaced = 954 mL.
Thus;
Density = 16500/954 = 17.3 g/mL
Now this value of 17.3 g/mL is lesser than that of pure gold given as 19.3 g/mL, it implies that the idol is not made of pure gold.
Determine the mass of the gold statue using its volume and density.
[tex]\to density = \frac{mass}{volume} \\ or \\ \to mass = density \times volume[/tex]
Converting the statue's volume from L to mL so that the volume unit and density unit correspond.
Calculating the mass of the statue:
[tex]\to 19.3\ \frac{g}{mL} \times 1000\ mL = 19,300\ g\\\\[/tex]
The weight of the sand must be the same as the weight of the statue, which is [tex]19,300\ g\\\\[/tex]
Calculate the volume of sand required using the mass and density of the sand.
[tex]\to density = \frac{mass}{volume} \\ or \\ \to mass = density \times volume[/tex]
Calculating the volume of required sand:
[tex]\to \frac{19,300\ g}{23 \ \frac{g}{mL}} = 8391\ mL \ or\ 8.391\ L[/tex]
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