A cube has a side length `1.2xx10^(-2)m`.Calculate its volume

Options

A. `1.7xx10^(-6)m^(3)`
B. `1.73xx10^(-6)m^(3)`
C. `1.70xx10^(-6)m^(3)`
D. `1.732xx10^(-6)m^(3)`

Answer

To calculate the volume of a cube with a given side length, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given side length of the cube**:
- The side length \( s \) is given as \( 1.2 \times 10^{-2} \, \text{m} \).

2. **Recall the formula for the volume of a cube**:
- The volume \( V \) of a cube is calculated using the formula:
\[ V = s^3 \]

3. **Substitute the given side length into the formula**:
- Substitute \( s = 1.2 \times 10^{-2} \, \text{m} \) into the volume formula:
\[ V = (1.2 \times 10^{-2})^3 \]

4. **Calculate \( (1.2)^3 \)**:
- Calculate \( 1.2 \times 1.2 \times 1.2 \):
\[ 1.2 \times 1.2 = 1.44 \]
\[ 1.44 \times 1.2 = 1.728 \]

5. **Calculate \( (10^{-2})^3 \)**:
- Using the exponent rule \( (a^m)^n = a^{m \cdot n} \):
\[ (10^{-2})^3 = 10^{-6} \]

6. **Combine the results**:
- Now, combine the results from steps 4 and 5:
\[ V = 1.728 \times 10^{-6} \, \text{m}^3 \]

7. **Apply significant figures**:
- The given side length \( 1.2 \) has one digit after the decimal point. Therefore, we should round \( 1.728 \) to one decimal place:
\[ V \approx 1.7 \times 10^{-6} \, \text{m}^3 \]

### Final Answer:
The volume of the cube is approximately:
\[ V \approx 1.7 \times 10^{-6} \, \text{m}^3 \]