Problem Solving

The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300 cm. If each of the three measurements has an error of at atmost 1 cm, which of the following is closest to the maximum possible difference, in cubic cm, between the actual capacity of the box and the capacity computed using these measurements?

1. 100,000
2. 120,000
3. 160,000
4. 240,000
5. 320,000

[spoiler]OA: C[/spoiler]

The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?

A - 100,000
B - 120,000
C - 160,000
D - 200,000
E - 320,000

Let L = 200, W = 200, and H = 300.
When each dimension changes by 1cm, the result is the following:

The LENGTH changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- W*H -- will change by 1cm:
1 * 200 * 300 = 60000.

The WIDTH changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- L*H -- will change by 1cm:
1 * 200 * 300 = 60000.

The HEIGHT changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- L*W -- will change by 1cm:
1 * 200 * 200 = 40000.

Note:
Because each dimension is included in 2 of the 3 products above, there is some OVERLAP among the 3 changes in volume.
Thus:
Approximate total change in volume = 60000 + 60000 + 40000 = 160000.

The correct answer is C.