Final answer:
The minimum volume of the tub is 28.04 cubic feet and the maximum volume is 38.56 cubic feet. The greatest possible percent error in calculating the volume is 30.6%.
Step-by-step explanation:
To find the minimum and maximum volumes of the tub, we need to consider the possible variations in the measurements. Since the measurements are given to the nearest half foot, we can assume a range of ±0.25 feet for each measurement. The minimum volume would be when each measurement is decreased by 0.25 feet, and the maximum volume would be when each measurement is increased by 0.25 feet.
Minimum volume:
Width = 3 - 0.25 = 2.75 feet
Length = 4 - 0.25 = 3.75 feet
Height = 2.5 - 0.25 = 2.25 feet
Volume = Width x Length x Height = 2.75 x 3.75 x 2.25 = 28.04 cubic feet
Maximum volume:
Width = 3 + 0.25 = 3.25 feet
Length = 4 + 0.25 = 4.25 feet
Height = 2.5 + 0.25 = 2.75 feet
Volume = Width x Length x Height = 3.25 x 4.25 x 2.75 = 38.56 cubic feet
The greatest possible percent error in calculating the volume of the tub can be found by comparing the uncertainty in volume to the actual volume. The uncertainty in volume can be calculated by finding the difference between the maximum and minimum volumes (38.56 - 28.04 = 10.52 cubic feet), and dividing it by the average of the maximum and minimum volumes (34.3 cubic feet).
Greatest percent error = (10.52 / 34.3) x 100 = 30.6%