Final answer:
The volume of the box is 9600cm³. The relative error in finding the volume is approximately 0.15625%.
Step-by-step explanation:
To find the volume of the box, we use the formula V = length * width * height. The given dimensions are length = 30cm, width = 16cm, and height = 20cm. Plugging these values into the formula, we get V = 30cm * 16cm * 20cm = 9600cm³.
To calculate the relative error in finding the volume, we need to determine the individual errors in each dimension. The error in length is 5cm, the error in width is 5cm, and the error in height is 5cm. Adding up these errors, we get a total error of 15cm.
The relative error is calculated by dividing the total error by the volume and multiplying by 100%. So, the relative error in finding the volume is (15cm / 9600cm³) * 100% ≈ 0.15625%.