The volume of a rectangular box is found by multiplying its length by its width and height. The correct calculations using the given dimensions in centimeters yield a volume of approximately 11.439 cm³. Uncertainties in measurement result in a small range of possible volumes around this central estimate.
The question involves finding the volume of a small box and understanding units and measurements in both the metric and imperial systems. To calculate the volume of a rectangular box, we multiply its length, width, and height. Given the measurements of the sides 1.80 cm, 2.05 cm, and 3.1 cm, the volume is calculated as follows:
Volume = length × width × height
Volume = 1.80 cm × 2.05 cm × 3.1 cm
Volume = 11.439 cm³ (rounded to three decimal places)
When calculating the volume with an uncertainty, we use the highest and lowest possible measurements based on the accuracy of the measuring device:
Lowest possible volume = (1.80 - 0.05) cm × (2.05 - 0.02) cm × (3.1 - 0.1) cm
Highest possible volume = (1.80 + 0.05) cm × (2.05 + 0.02) cm × (3.1 + 0.1) cm
Uncertainty = (Highest volume - Lowest volume) / 2
Uncertainty = (11.4 cm³ - Volume) where 11.4 cm³ is a rounded figure for the highest volume estimate based on provided accuracy.
The other statements concerning multiplying fractional inches to find the volume are not applicable as they do not align with the metric measurements provided. Likewise, the statement concerning the number of cubes to fill the box cannot be validated without additional information about the box's volume in cubic inches and the size of the cubes.