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

Options

A. `1.7xx10^(-6)m^(3)`
B. `1.73xx10^(-6)m^(3)`
C. `1.78xx10^(-6)m^(3)`
D. `1.732xx10^(-6)m^(3)`

Explanation

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

### Step 1: Identify the given length
The side length of the cube is given as:
\[ L = 1.2 \times 10^{-2} \, \text{m} \]

### Step 2: Write the formula for the volume of a cube
The volume \( V \) of a cube is calculated using the formula:
\[ V = L^3 \]

### Step 3: Substitute the value of \( L \) into the formula
Now, substituting the value of \( L \) into the volume formula:
\[ V = (1.2 \times 10^{-2})^3 \]

### Step 4: Calculate \( (1.2)^3 \)
First, calculate \( (1.2)^3 \):
\[ (1.2)^3 = 1.2 \times 1.2 \times 1.2 = 1.728 \]

### Step 5: Calculate \( (10^{-2})^3 \)
Next, calculate \( (10^{-2})^3 \):
\[ (10^{-2})^3 = 10^{-6} \]

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

### Step 7: Round off to significant figures
Since the original measurement of length \( L \) has two significant figures, we should round our volume to two significant figures as well:
\[ V \approx 1.7 \times 10^{-6} \, \text{m}^3 \]

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

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