Edge length of a cube is `1.7xx10^(-2)m`. What will be the volume of cube with correct significant digits?

Options

A. `4.913xx10^(-6)m^(3)`
B. `4.91xx10^(-6)m^(3)`
C. `4.9xx10^(-6)m^(3)`
D. `4.92xx10^(-6)m^(3)`

Explanation

To find the volume of a cube given the edge length, we can follow these steps:

### Step 1: Understand the formula for the volume of a cube
The volume \( V \) of a cube is calculated using the formula:
\[ V = a^3 \]
where \( a \) is the edge length of the cube.

### Step 2: Substitute the given edge length into the formula
Given the edge length \( a = 1.7 \times 10^{-2} \, \text{m} \), we can substitute this into the volume formula:
\[ V = (1.7 \times 10^{-2})^3 \]

### Step 3: Calculate the cube of the edge length
To calculate \( (1.7 \times 10^{-2})^3 \), we can break it down:
\[ V = 1.7^3 \times (10^{-2})^3 \]
Calculating \( 1.7^3 \):
\[ 1.7^3 = 1.7 \times 1.7 \times 1.7 = 4.913 \]
Calculating \( (10^{-2})^3 \):
\[ (10^{-2})^3 = 10^{-6} \]
Now, combine these results:
\[ V = 4.913 \times 10^{-6} \, \text{m}^3 \]

### Step 4: Determine the significant figures
The original edge length \( 1.7 \) has 2 significant figures. Therefore, the volume must also be reported with 2 significant figures.

### Step 5: Round the volume to the correct number of significant figures
The calculated volume is \( 4.913 \times 10^{-6} \). To round this to 2 significant figures:
- The first two digits are \( 4.9 \).
- The next digit is \( 1 \), which is less than 5, so we do not round up.

Thus, the volume of the cube, with the correct significant figures, is:
\[ V = 4.9 \times 10^{-6} \, \text{m}^3 \]

### Final Answer
The volume of the cube is \( 4.9 \times 10^{-6} \, \text{m}^3 \).

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