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

Options

A. radius
B. area
C. volume
D. none of these

Explanation

To solve the problem of determining where the maximum percentage change occurs when a copper sphere is heated, we will analyze the changes in radius, area, and volume step by step.

### Step 1: Understand the Physical Properties
When a copper sphere is heated, it expands. This expansion can be quantified in terms of changes in its radius, surface area, and volume.

### Step 2: Formulas for Area and Volume
1. **Surface Area (A)** of a sphere is given by the formula:
\[ A = 4\pi r^2 \]
2. **Volume (V)** of a sphere is given by the formula:
\[ V = \frac{4}{3}\pi r^3 \]

### Step 3: Calculate Percentage Change in Area
To find the percentage change in area with respect to the change in radius, we can use the following relationship:
\[ \frac{\Delta A}{A} = 2 \cdot \frac{\Delta r}{r} \]
This implies that the percentage change in area is:
\[ \text{Percentage change in A} = 2 \cdot \text{Percentage change in r} \]

### Step 4: Calculate Percentage Change in Volume
Similarly, for volume, we have:
\[ \frac{\Delta V}{V} = 3 \cdot \frac{\Delta r}{r} \]
This implies that the percentage change in volume is:
\[ \text{Percentage change in V} = 3 \cdot \text{Percentage change in r} \]

### Step 5: Compare the Changes
From the above relationships, we can see:
- The percentage change in area is proportional to \(2 \cdot \text{Percentage change in r}\).
- The percentage change in volume is proportional to \(3 \cdot \text{Percentage change in r}\).

### Step 6: Conclusion
Since the factor for volume (3) is greater than the factor for area (2), the maximum percentage change will occur in the volume of the sphere.

Thus, the answer to the question is that the maximum percentage change will be observed in the **volume** of the copper sphere.

### Final Answer
**Volume**

---