the edge of a cube was found to be 18 inches with a possible measurement error of 0.1 find the max possible error in calculating the surface area of the cube
6 * 18.1^2 = 1965.66
6 * 18^2 = 1944
difference = 21.66
That is the maximum possible error. The likely error is another subject entirely.
To find the maximum possible error in calculating the surface area of the cube, we need to consider the effect of the maximum possible measurement error on each edge.
The surface area of a cube is given by the formula: A = 6s^2, where A is the surface area and s is the length of one side or edge.
Given that the edge measurement is 18 inches with a possible error of 0.1 inches, we can calculate the maximum and minimum possible lengths of each edge.
Maximum possible length = 18 + 0.1 = 18.1 inches
Minimum possible length = 18 - 0.1 = 17.9 inches
Now we can calculate the maximum and minimum possible surface areas:
Maximum possible surface area = 6 (18.1)^2 square inches
Minimum possible surface area = 6 (17.9)^2 square inches
By calculating these two values, we can find the range of the possible surface area and determine the maximum error.
I will perform the calculations for you:
Maximum possible surface area = 6 (18.1)^2 = 1966.68 square inches
Minimum possible surface area = 6 (17.9)^2 = 1919.32 square inches
Thus, the maximum possible error in calculating the surface area of the cube is:
Max error = Maximum possible surface area - Minimum possible surface area
= 1966.68 - 1919.32
= 47.36 square inches
Therefore, the maximum possible error in calculating the surface area of the cube is approximately 47.36 square inches.