Final answer:
The correct answer is D. 6%, as the area of the base of a uniform metallic cylinder will increase by approximately 6% when the length increases by 3% due to uniform thermal expansion in all directions.
Step-by-step explanation:
The subject of the student's question is thermal expansion, which relates to how objects change in size across different dimensions as the temperature increases. When a uniform metallic cylinder is heated and its length increases by 3%, we can determine that the area of the base, which is a two-dimensional measure, will also increase due to the expansion in both dimensions (length and width).
For small changes in dimensions, the percentage increase in area due to thermal expansion can be approximated by doubling the linear expansion percentage, assuming the thermal expansion is uniform in all directions, thus leading to the conclusion that the area increases by approximately 6%.
The correct answer, therefore, to the question, 'On heating a uniform metallic cylinder, length increases by 3%. The area of cross-section of its base will increase by how much?' is D. 6%.