Let's work through each of the conversions step by step.
1. Convert 500 mm³ to cm³:
1 cm = 10 mm So, \(1 , \text{cm}^3 = (10 , \text{mm})^3 = 1000 , \text{mm}^3\).
To convert, we use: \[ 500 , \text{mm}^3 \times \frac{1 , \text{cm}^3}{1000 , \text{mm}^3} = \frac{500}{1000} , \text{cm}^3 = 0.5 , \text{cm}^3. \]
2. Convert 16,000,000 cm³ to m³:
1 m = 100 cm So, \(1 , \text{m}^3 = (100 , \text{cm})^3 = 1,000,000 , \text{cm}^3\).
To convert, we use: \[ 16,000,000 , \text{cm}^3 \times \frac{1 , \text{m}^3}{1,000,000 , \text{cm}^3} = \frac{16,000,000}{1,000,000} , \text{m}^3 = 16 , \text{m}^3. \]
3. Convert 4,000,000,000 m³ to km³:
1 km = 1,000 m So, \(1 , \text{km}^3 = (1000 , \text{m})^3 = 1,000,000,000 , \text{m}^3\).
To convert, we use: \[ 4,000,000,000 , \text{m}^3 \times \frac{1 , \text{km}^3}{1,000,000,000 , \text{m}^3} = \frac{4,000,000,000}{1,000,000,000} , \text{km}^3 = 4 , \text{km}^3. \]
4. Convert 10 cm³ to mm³:
Using the previous conversion: \[ 1 , \text{cm}^3 = 1000 , \text{mm}^3. \]
To convert, we use: \[ 10 , \text{cm}^3 \times \frac{1000 , \text{mm}^3}{1 , \text{cm}^3} = 10,000 , \text{mm}^3. \]
5. Convert 4 m³ to cm³:
Using the conversion from m³ to cm³: \[ 1 , \text{m}^3 = 1,000,000 , \text{cm}^3. \]
To convert, we use: \[ 4 , \text{m}^3 \times 1,000,000 , \text{cm}^3 = 4,000,000 , \text{cm}^3. \]
6. Convert 10 km³ to m³:
Using the conversion from km³ to m³: \[ 1 , \text{km}^3 = 1,000,000,000 , \text{m}^3. \]
To convert, we use: \[ 10 , \text{km}^3 \times 1,000,000,000 , \text{m}^3 = 10,000,000,000 , \text{m}^3. \]
Summary of Results:
- \(500 , \text{mm}^3 = 0.5 , \text{cm}^3\)
- \(16,000,000 , \text{cm}^3 = 16 , \text{m}^3\)
- \(4,000,000,000 , \text{m}^3 = 4 , \text{km}^3\)
- \(10 , \text{cm}^3 = 10,000 , \text{mm}^3\)
- \(4 , \text{m}^3 = 4,000,000 , \text{cm}^3\)
- \(10 , \text{km}^3 = 10,000,000,000 , \text{m}^3\)
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