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A room has an actual volume of 120 m³. A model of the room is built using a linear scale of 1:500. Calculate the volume of the model in cm³.

Mathematics

ScanSolve AI Answer

Answer

0.96 cm3\text{0.96 cm}^3

Step-by-step solution

3 steps

b)

  1. Determine the volume scale factor.

    The linear scale is 1:5001:500. For volumes, the scale factor is cubed.
    So, if the linear scale is 1:k1:k, the volume scale is 1:k31:k^3.
    Here, k=500k = 500.

    Volume scale factor=5003\text{Volume scale factor} = 500^3 Volume scale factor=500×500×500\text{Volume scale factor} = 500 \times 500 \times 500 Volume scale factor=125,000,000\text{Volume scale factor} = 125,000,000

    The volume scale is 1:125,000,0001:125,000,000.

  2. Calculate the volume of the room in the model.

    The actual volume of the room is 120 m3120 \text{ m}^3.
    To find the model volume, divide the actual volume by the volume scale factor.

    Model volume=Actual volumeVolume scale factor\text{Model volume} = \frac{\text{Actual volume}}{\text{Volume scale factor}} Model volume=120 m3125,000,000\text{Model volume} = \frac{120 \text{ m}^3}{125,000,000} Model volume=0.00000096 m3\text{Model volume} = 0.00000096 \text{ m}^3
  3. Convert the model volume from cubic meters to cubic centimeters.

    Since 1 m=100 cm1 \text{ m} = 100 \text{ cm}, then 1 m3=(100 cm)3=1,000,000 cm31 \text{ m}^3 = (100 \text{ cm})^3 = 1,000,000 \text{ cm}^3.

    Model volume in cm3=0.00000096 m3×1,000,000 cm3/m3\text{Model volume in cm}^3 = 0.00000096 \text{ m}^3 \times 1,000,000 \text{ cm}^3/\text{m}^3 Model volume in cm3=0.96 cm3\text{Model volume in cm}^3 = 0.96 \text{ cm}^3

    The corresponding volume of the model is 0.96 cm³.

    The corresponding volume of the model in cm3\text{cm}^3 is 0.96 cm3\boxed{\text{0.96 cm}^3}.

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