Final answer:
The volume of the rectangular prism is calculated by multiplying its length, width, and height, resulting in 11.451 cm³. The uncertainty is approximated at 0.15 cm³, leading to a reported volume of 11.4 ±0.1 cm³.
Step-by-step explanation:
To find the volume of a rectangular prism, you use the formula V = Length x Width x Height. Given the sides of the small rectangular box are 1.80 cm, 2.05 cm long, and 3.1 cm high, you multiply these dimensions to calculate the volume.
The volume of the rectangular prism is calculated by:
V = 1.80 cm x 2.05 cm x 3.1 cm = 11.451 cm³
To estimate the uncertainty in the calculated volume, we take the maximum possible error in each dimension, which is given as ±0.05 cm, and multiply this by the number of dimensions that have uncertainty, which in this case is three (Length, Width, and Height). So the absolute uncertainty in the volume is approximately:
Uncertainty = 3 x 0.05 cm = 0.15 cm³
Therefore, the volume of the box with its uncertainty is approximately 11.4 ±0.1 cm³, as indicated in the question.