When an iron ball is heated, it undergoes thermal expansion. The percentage increase in various dimensions can be analysed using the concepts of linear, area, and volume expansion.

Let's consider the following:

1.Linear Expansion (Diameter): The linear expansion can be described by the formula:

ΔL=αLΔT

where α is the coefficient of linear expansion, $L$ is the original length (diameter in this case), and ΔT is the change in temperature.

2.Area Expansion (Surface Area): The area expansion is given by:

ΔA=2αAΔT

where $A$ is the original surface area.

3.Volume Expansion (Volume): The volume expansion is given by:

ΔV=3αVΔT

where V is the original volume.

Let's consider the percentage increase for each case:

Diameter: The percentage increase in diameter is αΔT×100%

Surface Area: The percentage increase in surface area is 2αΔT×100%

Volume: The percentage increase in volume is 3αΔT×100

Since the coefficient of linear expansion α is the same for the material in all cases, we can compare the factors:

The factor for diameter is $1$.

The factor for surface area is $2$.

The factor for volume is $3$.

Thus, the percentage increase will be largest in the volume, as it has the largest multiplying factor of $3$.

The correct answer is option a. volume

When an iron ball is heated, it expands. The percentage increase in volume will be the largest because volume expansion involves a cubic relationship with temperature change, whereas linear expansion involves a linear relationship and area expansion involves a square relationship. Therefore, the volume increase has the highest percentage change.

When an iron ball is heated, it undergoes thermal expansion. The percentage increase in various dimensions can be analysed using the concepts of linear, area, and volume expansion.

Let's consider the following:

1.Linear Expansion (Diameter): The linear expansion can be described by the formula:

ΔL=αLΔT

where α is the coefficient of linear expansion, $L$ is the original length (diameter in this case), and ΔT is the change in temperature.

2.Area Expansion (Surface Area): The area expansion is given by:

ΔA=2αAΔT

where $A$ is the original surface area.

3.Volume Expansion (Volume): The volume expansion is given by:

ΔV=3αVΔT

where V is the original volume.

Let's consider the percentage increase for each case:

Diameter: The percentage increase in diameter is αΔT×100%

Surface Area: The percentage increase in surface area is 2αΔT×100%

Volume: The percentage increase in volume is 3αΔT×100

Since the coefficient of linear expansion α is the same for the material in all cases, we can compare the factors:

The factor for diameter is $1$.

The factor for surface area is $2$.

The factor for volume is $3$.

Thus, the percentage increase will be largest in the volume, as it has the largest multiplying factor of $3$.

The correct answer is option a. volume

When an iron ball is heated, it expands. The percentage increase in volume will be the largest because volume expansion involves a cubic relationship with temperature change, whereas linear expansion involves a linear relationship and area expansion involves a square relationship. Therefore, the volume increase has the highest percentage change.