imhimanshu wrote:
The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm 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
The options are well spread so we can approximate.
Changing the length by 1 cm results in change of the volume by 1*200*300 = 60,000 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 200*1*300 = 60,000 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 200*200*1 = 40,000 cubic centimeters.
So, approximate maximum possible difference is 60,000 + 60,000 + 40,000 = 160,000 cubic centimeters.
Answer: C.
Thanks for this explanation. I had set an algebraic approach and I wanted to take out common factor but at some point I didn´t know how to go on.
I know that the 200 of both the computed capacity and the actual capacity can be factored out, but I don´t know how to go on.
Would you please help here? I know that this can be helpful for other similar questions.