When a copper sphere is heated, maximum percentage change will be observed in :

Options

A. maximum in radius
B. maximum in volume
C. maximum in density
D. equal in radius, volume and density

Answer

To determine the maximum percentage change observed in a copper sphere when it is heated, we need to analyze how the radius, volume, and density of the sphere change with temperature.

### Step-by-Step Solution:

1. **Understand the Problem**:
- We need to find out which of the following properties of a copper sphere changes the most when it is heated: radius, volume, or density.

2. **Identify the Relevant Formulas**:
- The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
- The density \( \rho \) of a sphere is given by the formula:
\[ \rho = \frac{m}{V} \]
- Here, \( m \) is the mass of the sphere, which remains constant as the sphere is heated.

3. **Analyze the Change in Radius**:
- When the sphere is heated, the radius \( r \) increases. The change in radius can be expressed as a percentage change:
\[ \text{Percentage change in radius} = \frac{\Delta r}{r} \times 100\% \]

4. **Analyze the Change in Volume**:
- Since the volume is proportional to the cube of the radius, if the radius increases, the volume will increase significantly:
\[ V \propto r^3 \]
- Therefore, the percentage change in volume can be calculated as:
\[ \text{Percentage change in volume} = \frac{\Delta V}{V} \times 100\% \]

5. **Analyze the Change in Density**:
- The density is inversely proportional to the volume:
\[ \rho \propto \frac{1}{r^3} \]
- As the volume increases with the increase in radius, the density will decrease. The percentage change in density can be expressed as:
\[ \text{Percentage change in density} = \frac{\Delta \rho}{\rho} \times 100\% \]

6. **Determine the Maximum Change**:
- Since the volume changes with the cube of the radius, the percentage change in volume will be greater than the percentage change in radius.
- The density decreases as the volume increases, but the percentage change in density will be less than that of volume due to its inverse relationship with volume.

7. **Conclusion**:
- After analyzing the changes, we conclude that the maximum percentage change will be observed in the volume of the copper sphere when it is heated.

### Final Answer:
The maximum percentage change will be observed in the **volume** of the copper sphere.