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An engineer is working with archeologists to create a realistic Roman village in a museum. The plan for a balance in a marketplace calls for granite stones, each weighing denarium. (The denarium was a Roman unit of mass: ). The manufacturing process for making the stones will remove of the material. If the granite to be used has a density of , what is the minimum volume of granite (in ) that the engineer should order?

Respuesta :

Answer:

The minimum volume requirement for the granite stones is 1543.64 cm³

Explanation:

1 granite stone weighs 10 denarium

100 granted stones will weigh 1000 denarium

1 denarium = 3.396g

1000 denarium = 3396g.

But we're told that 20% of material is lost during the making of these stones.

This means the mass calculated represents 80% of the original mass requirement, m.

80% of m = 3396

m = 3396/0.8 = 4425 g

This mass represents the minimum mass requirement for making the stones.

To now obtain the corresponding minimum volume requirement

Density = mass/volume

Volume = mass/density = 4425/2.75 = 1543.64 cm³

Hope this helps!!!

fichoh

Using the mass - density relationship, the minimum volume of granite that should be ordered is 1543.6 cm³

Given the Parameters :

  • 1 granite Stone = 10 denarium
  • 100 granite stones = (100 × 10) = 1000 denarium
  • 1 denarium = 3.396 g

Hence,

1000 denarium = (1000 × 3.396) = 3396 grams

Since 20% of materials will be removed :

  • Let total percentage material = p

(100p - 20p)% = 80% = 0.8p

0.8p = 3396 grams

Divide both sides by 0.8

p = 3396 / 0.8

p = 4245 grams

Recall :

  • Density = Mass / Volume

2.75 = 4245 / Volume

Volume = 4245/2.75

Volume = 1543.6 cm³

Hence, the minimum volume of granite required is 1543.6 cm³

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