Answer:
A) possible error = 12.992
Possible values for the volume [1715,007,1740.992]
B) possible error = 4.325
Possible values for the surface area [859,675,868,325]
Step-by-step explanation:
The volumen of a cube is the cube of the length of a side. Thus, the meassurement of the volume is 12³ = 1728 inches³. To calculate the error, lets call Y the real value of the length,
Y = X + e, where e is the error and X = 12.
Y³ = (X+e)³ = X³ + 3X²e + 3Xe² + e³
the error is 0.03 inches, so we have that
Y³ = X³ + 12.96+0.0324+ 0.000027 = X³+12.992427 = X³+12.992 (rounded to 3 decimal places).
Thus, the absolute possible error is Y³- X³ = 12.992, and the volume of the cube is contained in the interval [X³-12.992,X³+12.992] = [1715,007,1740.992]
B) The surface area is 6 X². With X meassured as 12, the surface area is meassured by 6*12² = 864.
To calculate the absolute error, we take Y = X+e, with X and e as before. We have
6 Y² = 6*(X+e)² = 6X²+12Xe+6e² = 6X²+4.32+0.0054 = 6X²+4.3254
Hence, the absolute error is bounded by 6Y²-6X² = 4.3254 rounded by 4.325, and the value of the surface area is contained in the interval [6X² -4.325, 6X²+4.325] = [859,675, 868,325]
