Final answer:
To calculate the volume of an open box with a rectangular base, multiply the length, width, and height. For a box with given dimensions and uncertainties, the volume is approximately 11.46 cm³ with an uncertainty of ± 0.1 cm³.
Step-by-step explanation:
To determine the dimensions of a constructed open box with a rectangular base, we must consider the volume of the box and the accuracy of the measurements involved. For instance, let's calculate the volume and uncertainty for a box with sides measured to be 1.80 ± 0.01 cm, 2.05 ± 0.02 cm, and height 3.1 ± 0.1 cm.
The volume V is given by the product of the length L, width W, and height H:
V = L × W × H
So, V = 1.80 cm × 2.05 cm × 3.1 cm = 11.457 cm³, which we can round to V = 11.46 cm³ based on the significant figures.
The maximum uncertainty in the volume can be estimated using the product of relative uncertainties:
- Relative uncertainty of length = 0.01/1.80
- Relative uncertainty of width = 0.02/2.05
- Relative uncertainty of height = 0.1/3.1
Add up the relative uncertainties and multiply by the calculated volume:
Maximum Uncertainty = (Relative uncertainty of length + Relative uncertainty of width + Relative uncertainty of height) × Volume
When rounded to the appropriate number of significant figures, this yields an uncertainty of about ± 0.1 cm³. Hence, the volume of the box is approximately 11.46 cm³ with an uncertainty of ± 0.1 cm³.