Question

Convert between the units of volume
500mm cubed = cm cubed
16000000cm cubed=m cubed
4000000000m cubed=km cubed
10cm cubed=mm cubed
4mcubed = cm cubed
10km cubed= m cubed

Answer 1

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:
- \(500 \, \text{mm}^3 = 0.5 \, \text{cm}^3\)
- \(16,000,000 \, \text{cm}^3 = 16 \, \text{m}^3\)
- \(4,000,000,000 \, \text{m}^3 = 4 \, \text{km}^3\)
- \(10 \, \text{cm}^3 = 10,000 \, \text{mm}^3\)
- \(4 \, \text{m}^3 = 4,000,000 \, \text{cm}^3\)
- \(10 \, \text{km}^3 = 10,000,000,000 \, \text{m}^3\)