The length, breadth and thickness of a strip are given by `l = (10.0 +- 0.1) cm, h = (1.00 +- 0.01) cm, t = (0.100 +- 0.001) cm`. The most probable error in volume will be

Options

A. `pm 0.03 cm^(3)`
B. `pm 0.111 cm^(3)`
C. `pm 0.012 cm^(3)`
D. none of these

Explanation

To find the most probable error in the volume of the strip given the measurements for length (l), breadth (h), and thickness (t), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Measurements and Their Errors**:
- Length (l) = \(10.0 \pm 0.1 \, \text{cm}\)
- Breadth (h) = \(1.00 \pm 0.01 \, \text{cm}\)
- Thickness (t) = \(0.100 \pm 0.001 \, \text{cm}\)

2. **Calculate the Volume (V)**:
The volume \(V\) of the strip can be calculated using the formula:
\[ V = l \times h \times t \]
Substituting the values:
\[ V = 10.0 \, \text{cm} \times 1.00 \, \text{cm} \times 0.100 \, \text{cm} = 1.00 \, \text{cm}^3 \]

3. **Calculate the Relative Errors**:
The relative error in volume is given by:
\[ \frac{\Delta V}{V} = \frac{\Delta l}{l} + \frac{\Delta h}{h} + \frac{\Delta t}{t} \]
Where:
- \(\Delta l = 0.1 \, \text{cm}\)
- \(\Delta h = 0.01 \, \text{cm}\)
- \(\Delta t = 0.001 \, \text{cm}\)

4. **Substituting the Values**:
Now, we substitute the values into the equation:
\[ \frac{\Delta V}{V} = \frac{0.1}{10.0} + \frac{0.01}{1.00} + \frac{0.001}{0.100} \]
Calculating each term:
- \(\frac{0.1}{10.0} = 0.01\)
- \(\frac{0.01}{1.00} = 0.01\)
- \(\frac{0.001}{0.100} = 0.01\)

5. **Summing the Relative Errors**:
Adding these relative errors together:
\[ \frac{\Delta V}{V} = 0.01 + 0.01 + 0.01 = 0.03 \]

6. **Calculating the Absolute Error in Volume**:
Now, to find the absolute error in volume \(\Delta V\):
\[ \Delta V = V \times \frac{\Delta V}{V} = 1.00 \, \text{cm}^3 \times 0.03 = 0.03 \, \text{cm}^3 \]

7. **Final Result**:
Therefore, the most probable error in the volume is:
\[ \Delta V = \pm 0.03 \, \text{cm}^3 \]

### Summary:
The most probable error in the volume of the strip is \( \pm 0.03 \, \text{cm}^3 \).