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7. A bronze statue is 4.5 m high and has a mass of 195,200 kg. The density of bronze is 8000 kg/m³. The volume of a mathematically similar model of the statue is 0.385 m³.

Calculate the height of the model.

[Density = Mass / Volume]

Answer :

Answer:

about 1.129 m

Step-by-step explanation:

You want the height of a model bronze statue with a volume of 0.385 m³ if it is similar to one 4.5 m high with a mass of 195,200 kg, given bronze has a density of 8000 kg/m³.

Volume

The volume of the full-size statue is ...

Volume = mass/density

Volume = (195,200 kg)/(8000 kg/m³) = 24.4 m³

Height

The ratio of volumes is the cube of the ratio of heights:

(h/4.5)³ = (0.385/24.4)

h = ∛(0.385/24.4) · 4.5 ≈ 1.129 . . . . . meters

The model statue is about 1.129 meters high.

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