The side of a cube, as measured with a vernier calipers of least count 0.01 cm is 3.00 cm. The maximum possible error in the measurement of volume is

Options

A. `pm 0.01 cm^3`
B. `pm 0.06 cm^3`
C. `pm 0.0 cm^3`
D. `pm 0.27 cm^3`

Answer

To find the maximum possible error in the measurement of the volume of a cube, we can follow these steps:

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

### Step 2: Identify the given values
From the problem, we have:
- Side length \( a = 3.00 \, \text{cm} \)
- Least count of the Vernier calipers (which represents the maximum possible error in the measurement of side) \( dA = 0.01 \, \text{cm} \)

### Step 3: Differentiate the volume formula
To find the maximum possible error in volume \( dV \), we differentiate the volume formula with respect to \( a \):
\[ dV = \frac{dV}{da} \cdot da = 3a^2 \cdot dA \]

### Step 4: Substitute the values into the differentiated formula
Now, substituting \( a = 3.00 \, \text{cm} \) and \( dA = 0.01 \, \text{cm} \):
\[ dV = 3 \cdot (3.00)^2 \cdot (0.01) \]
Calculating \( (3.00)^2 \):
\[ (3.00)^2 = 9.00 \]
Now substituting back:
\[ dV = 3 \cdot 9.00 \cdot 0.01 \]

### Step 5: Calculate the maximum possible error in volume
Now, calculate \( dV \):
\[ dV = 27 \cdot 0.01 = 0.27 \, \text{cm}^3 \]

### Conclusion
The maximum possible error in the measurement of volume is:
\[ \pm 0.27 \, \text{cm}^3 \]