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.
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