]So, the total volume of the cube is 216m³ with an uncertainty of ±22.749m³.
Explanation:
To calculate the total volume of the cube and its uncertainty, we first find the volume using the formula for the volume of a cube, which is given by:[ V = s^3 ]Where ( s ) is the length of a side of the cube.Given that the length of each side ( s ) is 6m with an uncertainty of ±0.2m, we can calculate the volume as follows:[ V = (6m)^3 = 216m^3 ]Next, we calculate the maximum and minimum possible volumes by adding and subtracting the uncertainty from the side length:[ \text{Maximum volume} = (6 + 0.2)^3 = 6.2^3 = 240.61m^3 ][ \text{Minimum volume} = (6 - 0.2)^3 = 5.8^3 = 195.112m^3 ]Now, to find the uncertainty in the volume, we take half the difference between the maximum and minimum volumes:[ \text{Uncertainty} = \frac{\text{Maximum volume} - \text{Minimum volume}}{2} ][ \text{Uncertainty} = \frac{240.61m^3 - 195.112m^3}{2} ][ \text{Uncertainty} = \frac{45.498m^3}{2} ][ \text{Uncertainty} = 22.749m^3 ]So, the total volume of the cube is 216m³ with an uncertainty of ±22.749m³.
