The measurements obtained for the interior dimensions of a rectangular box are 60 cm by 60 cm by 90 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?
Choose the most appropriate option.
A) 14,500 B) 14,600 C) 14,400 D) 14,700 E) 14,800
The options are well spread so we can approximate.   Changing the length by 1 cm results in change of the volume by 1*60*90= 
<gadget id="calculator">1*60*90</gadget>
<output>5_400</output>
5400 cubic centimeters;   Changing the width by 1 cm results in change of the volume by 60*1*90= 
<gadget id="calculator">60*1*90</gadget>
<output>5_400</output>
5400 cubic centimeters;   Changing the height by 1 cm results in change of the volume by 60*60*1= 
<gadget id="calculator">60*60*1</gadget>
<output>3_600</output>
3600 cubic centimeters.   So, approximate maximum possible difference is 5400 + 5400 + 3600= 14,400 cubic centimeters.   Answer: 14,400
<result>C</result>
The measurements obtained for the interior dimensions of a rectangular box are 60 cm by 60 cm by 90 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?