Which of these is the correct relationship between liter and `mm^(3)`?

Options

A. `1"liter" = 10^(3) mm^(3)`
B. `1"liter" = 10^(4) mm^(3)`
C. `1"liter" = 10^(5) mm^(3)`
D. `1"liter" = 10^(6) mm^(3)`

Answer

To find the correct relationship between liters and cubic millimeters (mm³), we can follow these steps:

### Step 1: Understand the Units
- A liter (L) is a unit of volume.
- A cubic millimeter (mm³) is also a unit of volume, derived from the millimeter, which is a unit of length.

### Step 2: Conversion Factors
- We know that 1 liter is equivalent to 1000 cubic centimeters (cm³).
- Additionally, we know that 1 cm is equal to 10 mm. Therefore, 1 cm³ is equal to (10 mm)³.

### Step 3: Calculate the Volume in mm³
- Since 1 cm = 10 mm, we can calculate:
\[ 1 \text{ cm}^3 = (10 \text{ mm})^3 = 10^3 \text{ mm}^3 = 1000 \text{ mm}^3 \]
- Therefore, 1 liter (which is 1000 cm³) can be converted to mm³:
\[ 1 \text{ L} = 1000 \text{ cm}^3 = 1000 \times 1000 \text{ mm}^3 = 10^6 \text{ mm}^3 \]

### Step 4: Final Relationship
- Thus, we conclude that:
\[ 1 \text{ L} = 10^6 \text{ mm}^3 \]

### Step 5: Identify the Correct Option
- Based on our calculation, the correct relationship is that 1 liter is equal to \(10^6\) cubic millimeters (mm³). Therefore, the correct option is option D.