... A standard backpack is approximately 30cm x 30cm x 40cm. Suppose you find a hoard of pure gold while treasure hunting in the wilderness. How
much mass would your backpack hold if you filled it with the gold? An
average student has a mass of 70 kg. How do these values compare?

1) The mass that the backpack can hold when filled with gold is 694.8 kg of gold

2) The mass of the backpack is approximately 9.93 times the mass of an average student

Explanation:

1) The given information are;

The dimension of the backpack = 30 cm × 30 cm × 40 cm

The mass of an average student = 70 kg

The volume of the backpack = 30 cm × 30 cm × 40 cm = 36000 cm³

The density of gold = 19.3 g/cm³

Therefor, the mass of the gold is given by the relation;

Density = Mass/Volume

Mass = Density × Volume

The mass of the pure gold = 19.3 g/cm³ × 36000 cm³ = 694,800 grams

1,000 grams = 1 kilogram = 1 kg

694,800 grams = 694,800 grams/(1,000 grams)×1 kg = 694.8 kg

The mass that the backpack can hold when filled with gold = 694.8 kg

2) Given that the mass of an average student = 70 kg, we have;

The mass of the bag of gold is 694.8 kg/(70 kg) or approximately 9.93 times heavier than the average student

The mass of the backpack is approximately 9.93 times the mass of an average student.

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