A solid metal ball has a spherical cavity. If the ball is heated, the volume of the cavity will

Options

A. increase
B. decreases
C. remain uncharged
D. Data insufficient

Explanation

To solve the problem, we need to analyze the effect of heating on a solid metal ball that contains a spherical cavity. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Structure
We have a solid metal ball with a spherical cavity inside it. Let’s denote the radius of the metal ball as \( r_2 \) and the radius of the cavity as \( r_1 \).

### Step 2: Heating the Metal Ball
When the metal ball is heated, the temperature of the entire ball increases. As a result, the metal expands due to thermal expansion.

### Step 3: Effect of Thermal Expansion
Thermal expansion affects all parts of the metal ball, including the cavity. The metal expands outward, which means that the radius of the metal ball \( r_2 \) will increase.

### Step 4: Impact on the Cavity
Since the cavity is part of the metal ball, as the metal expands, the cavity will also expand. This means that the radius of the cavity \( r_1 \) will also increase.

### Step 5: Volume Calculation
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
As the radius \( r_1 \) of the cavity increases due to the expansion, the volume of the cavity will also increase.

### Conclusion
Therefore, when the solid metal ball is heated, the volume of the cavity will increase.

### Final Answer
The volume of the cavity will **increase**.

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