TeXes Science Practice Test

When a large metallic sphere is heated, which property shows the largest percentage increase?

1. Surface area

2. Diameter

3. Mass

4. Volume

The correct answer is: Volume

When a large metallic sphere is heated, the property that shows the largest percentage increase is volume. This is primarily due to the thermal expansion properties of materials. As the temperature of the sphere increases, the individual atoms within the metal vibrate more vigorously, leading to an increase in distance between them. This results in an expansion of the material in all directions. For a spherical object, this expansion affects the volume more significantly than it does the surface area or linear dimensions like diameter. In geometric terms, the volume of a sphere is calculated using the formula \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius. Given that volume depends on the cube of the radius, any increase in radius, due to thermal expansion, causes the volume to increase at a cubic rate. In contrast, diameter increases linearly, and even though the surface area (which is proportional to the square of the radius) increases as well, these increases do not match the percentage increase in volume resulting from the same temperature rise. Therefore, when considering thermal expansion, the volume tends to exhibit the largest percentage increase compared to the other properties when a metallic sphere is heated.