The measurements obtained for the interior dimensions of a rectangular box are 120 cm by 120 cm by 180 cm. 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? Pick one:
A) 55,600 B) 53,600 C) 54,600 D) 58,600 E) 57,600
The options are well spread so we can approximate.   Changing the length by 1 cm results in change of the volume by 1*120*180= 
<gadget id="calculator">1*120*180</gadget>
<output>21_600</output>
21600 cubic centimeters;   Changing the width by 1 cm results in change of the volume by 120*1*180= 
<gadget id="calculator">120*1*180</gadget>
<output>21_600</output>
21600 cubic centimeters;   Changing the height by 1 cm results in change of the volume by 120*120*1= 
<gadget id="calculator">120*120*1</gadget>
<output>14_400</output>
14400 cubic centimeters.   So, approximate maximum possible difference is   21600 + 21600 + 14400= 
<gadget id="calculator">  21600 + 21600 + 14400</gadget>
<output>57_600</output>
57600 cubic centimeters.   Answer: 57,600
<result>E</result>
The measurements obtained for the interior dimensions of a rectangular box are 120 cm by 120 cm by 180 cm. 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?