In the measurement of volume of solid sphere using the formula `V=(4)/(3) pir^(3)` if the error committed in the measurement of the radius r is 1.5%, the percentage error in the volume measurement is

Options

A. `3%`
B. `1.5%`
C. `4.5%`
D. `0.75%`

Answer

To find the percentage error in the volume measurement of a solid sphere when the error in the radius measurement is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The volume \( V \) of a solid sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Here, \( r \) is the radius of the sphere.

2. **Identify the Relationship**: The volume \( V \) is proportional to the cube of the radius \( r \):
\[ V \propto r^3 \]

3. **Given Percentage Error in Radius**: We are given that the percentage error in the measurement of the radius \( r \) is 1.5%. This can be expressed as:
\[ \frac{\Delta r}{r} \times 100\% = 1.5\% \]
where \( \Delta r \) is the absolute error in the radius.

4. **Calculate the Percentage Error in Volume**: The relationship between the percentage error in volume and the percentage error in radius can be derived from the formula. Since volume is proportional to \( r^3 \), the percentage error in volume \( \frac{\Delta V}{V} \) can be expressed as:
\[ \frac{\Delta V}{V} \times 100\% = 3 \left(\frac{\Delta r}{r} \times 100\%\right) \]

5. **Substitute the Given Error**: Now, substituting the given percentage error of the radius into the equation:
\[ \frac{\Delta V}{V} \times 100\% = 3 \times 1.5\% = 4.5\% \]

6. **Final Result**: Therefore, the percentage error in the volume measurement is:
\[ \text{Percentage error in volume} = 4.5\% \]

### Conclusion:
The percentage error in the volume measurement of the solid sphere is **4.5%**.