One side of a cube is measured as `a=4.03pm 1%`. What is its value?

Options

A. `65.45m^(3)pm1%`
B. `65.45m^(3)pm2%`
C. `65.45m^(3) pm 3%`
D. `65.45m^(3)pm4%`

Explanation

To solve the problem, we need to calculate the volume of a cube given the side length and its uncertainty. The side length \( a \) is given as \( 4.03 \, \text{pm} \) with a \( 1\% \) uncertainty.

### Step-by-Step Solution:

1. **Identify the given values**:
- Side length \( a = 4.03 \, \text{pm} \)
- Uncertainty = \( 1\% \)

2. **Calculate the volume of the cube**:
The formula for the volume \( V \) of a cube is given by:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = (4.03 \, \text{pm})^3 \]

3. **Calculate \( 4.03^3 \)**:
\[ 4.03^3 = 4.03 \times 4.03 \times 4.03 \approx 65.45 \, \text{pm}^3 \]

4. **Calculate the uncertainty in volume**:
The uncertainty in volume due to the uncertainty in side length can be calculated using the formula:
\[ \Delta V = 3 \times V \times \frac{\Delta a}{a} \]
Here, \( \Delta a \) is the uncertainty in \( a \). Since the uncertainty is \( 1\% \):
\[ \Delta a = 0.01 \times 4.03 \, \text{pm} = 0.0403 \, \text{pm} \]
Now substituting the values:
\[ \Delta V = 3 \times 65.45 \, \text{pm}^3 \times \frac{0.0403 \, \text{pm}}{4.03 \, \text{pm}} \]

5. **Calculate \( \Delta V \)**:
\[ \Delta V = 3 \times 65.45 \times 0.00996 \approx 1.96 \, \text{pm}^3 \]

6. **Final result**:
The value of the volume with its uncertainty is:
\[ V = 65.45 \, \text{pm}^3 \pm 1.96 \, \text{pm}^3 \]

### Summary:
The volume of the cube is \( 65.45 \, \text{pm}^3 \) with an uncertainty of \( \pm 1.96 \, \text{pm}^3 \).