The measurements obtained for the interior dimensions of a rectangular box are 100 cm by 100 cm by 150cm. 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? Choose the correct choice:
A) 50,000	B) 40,000	C) 45,000	D) 50,000	E) 60,000
The options are well spread so we can approximate.   Changing the length by 1 cm results in change of the volume by 1*100*150 = 15,000 cubic centimeters;   Changing the width by 1 cm results in change of the volume by 100*1*150 = 15,000 cubic centimeters;   Changing the height by 1 cm results in change of the volume by 100*100*1 = 10,000 cubic centimeters.   So, approximate maximum possible difference is 15,000 + 15,000 + 10,000 = 40,000 cubic centimeters.   Answer: 40,000.
<result>B</result>
The measurements obtained for the interior dimensions of a rectangular box are 100 cm by 100 cm by 150cm. 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?