Answer:
The volume of a cube is given by the formula V = s^3, where s is the length of a side of the cube. In this case, the length of a side is 11.4 centimeters with a possible error of + - 0.04 centimeters.
To find the possible error in the value of the volume of the cube, we can use the formula for the maximum error in a product:
max error in V = |V| * (max error in s / s)
where |V| is the absolute value of the volume, and max error in s is the maximum possible error in the measurement of the side.
Substituting the given values, we get:
max error in V = |11.4^3| * (0.04 / 11.4)
max error in V = 538.516 * 0.00351
max error in V = 1.89 cubic centimeters (rounded to two decimal places)
Therefore, the estimate for the possible error in the value of the volume of the cube is 1.89 cubic centimeters