Final answer:
The volume of the rectangular prism is approximately 16.8 cm³ with an uncertainty of approximately 1.165 cm³.
Step-by-step explanation:
The volume of the rectangular prism can be calculated by multiplying its length, width, and height. In this case, the height is 4 cm, the base is 1.4 cm, and the width is 3 cm. So, the volume formula is:
Volume = Length x Width x Height
Plugging in the given dimensions, we get:
Volume = 1.4 cm x 3 cm x 4 cm = 16.8 cm³
The uncertainty of the volume can be calculated by considering the uncertainties in each dimension. Since the measuring device is accurate to ±0.05 cm, the uncertainties for the length, width, and height are all ±0.05 cm. To calculate the uncertainty in the volume, we can use the following formula:
Uncertainty in Volume = Length x Width x Height x Total Relative Uncertainty
Since the total relative uncertainty is the sum of the individual relative uncertainties:
Total Relative Uncertainty = (Relative Uncertainty in Length) + (Relative Uncertainty in Width) + (Relative Uncertainty in Height)
Plugging in the values, we get:
Total Relative Uncertainty = (0.05 cm/1.4 cm) + (0.05 cm/3 cm) + (0.05 cm/4 cm) = 0.0694
Finally, we can calculate the uncertainty in the volume:
Uncertainty in Volume = 16.8 cm³ x 0.0694 ≈ 1.165 cm³
Therefore, the volume of the rectangular prism is approximately 16.8 cm³ with an uncertainty of approximately 1.165 cm³.