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.
Why is the difference not (201x201x301)-(199x199x299)? Is it because of this wording: "each of the three measurements has an error of at most 1 centimeter"? Therefore, the difference between the actual and given dimensions can be max. 1cm?
The wording is different from saying that a measurement has a margin of error of 1cm, which would mean that the difference could be +/- 1cm from the given values, correct?