Final answer:
The volume of a rectangular solid with a square base is calculated by squaring the side length of the base and multiplying by the height. For a given box with dimensions, multiply length, width, and height to get the volume. Estimating the uncertainty involves understanding the accuracy of each measurement.
Step-by-step explanation:
To calculate the volume of a rectangular solid with a square base and a given volume of 1728 cubic inches, we must find the length of the sides of the square base and the height of the solid. The volume of a rectangular solid is determined by the formula volume = length x width x height. Since the base is square, length and width are equal. Let's denote the side of the square base as 's' and the height as 'h'. Therefore, the volume can also be expressed as s x s x h = 1728. To find the precise measurements of the base and height, we would typically need more information. However, if we're provided with any two dimensions, we can solve for the third using the volume.
For a rectangular box measured to be 1.80 cm by 2.05 cm by 3.1 cm, the volume can be calculated simply by multiplying these dimensions: volume = 1.80 cm x 2.05 cm x 3.1 cm. To estimate the uncertainty, assuming an accuracy of ±0.05 cm for each measurement, one would use the method of partial derivatives or approximation methods to determine the potential variation in volume based on these uncertainties.