If the scale model of a cube sculpture is 0.5 cm per every 1 m of the real sculpture, what is the volume of the model, If the volume of the real sculpture is `64m^(3)`?

Answer

To find the volume of the scale model of a cube sculpture given the volume of the real sculpture, we can follow these steps:

### Step 1: Understand the scale conversion
The scale model is given as 0.5 cm for every 1 m of the real sculpture. This means:
- 1 m = 0.5 cm.

### Step 2: Convert the volume of the real sculpture to the scale model's volume
The volume of the real sculpture is given as 64 m³. Since the volume of a cube is calculated as side³, we need to convert the dimensions from meters to centimeters using the scale conversion.

### Step 3: Calculate the side length of the real sculpture
To find the side length of the real cube sculpture, we take the cube root of the volume:
\[ \text{Side length of real sculpture} = \sqrt[3]{64 \, \text{m}^3} = 4 \, \text{m} \]

### Step 4: Convert the side length to the scale model
Now, we convert the side length from meters to centimeters using the scale:
\[ \text{Side length of model} = 4 \, \text{m} \times \left(\frac{0.5 \, \text{cm}}{1 \, \text{m}}\right) = 4 \times 0.5 \, \text{cm} = 2 \, \text{cm} \]

### Step 5: Calculate the volume of the scale model
Now that we have the side length of the scale model, we can calculate its volume:
\[ \text{Volume of model} = \text{Side length}^3 = (2 \, \text{cm})^3 = 2 \times 2 \times 2 = 8 \, \text{cm}^3 \]

### Final Answer
The volume of the scale model of the sculpture is \(8 \, \text{cm}^3\).

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