By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 meters, inclusive, the breadth is between 1 to 1.1 meters, inclusive and the height is between 2 to 2.1 centimeters, inclusive. If the actual length, breadth and height of the box do indeed fall within the respective ranges estimated by the carpenter, which of the following is the closest to the maximum possible magnitude of the percentage error W that the carpenter can make in calculating the volume of the rectangular box? Choose the correct choice from the following choices:
A) 1% B) 3% C) 10% D) 18% E) 22%
the dimensions are between 2-2.1, 1-1.1 and 2-2.1..   so MAX error in Volume=?..   IMPORTANT POINTS TO NOTE   1) Max ERROR would be when actuals and estimate are at the extreme ends..   2) BUT what about MAX % ERROR--   It will be when the base is the lowest...   so the ACTUALS should be lowest or at lower end and the ESTIMATE at the higher end..   SOLUTION   Actuals= 2*2*1=4..   Estimate=2.1*2.1*1.1=4.841..   Max % error W=(4.841-4)/4 *100= 84.1/4 = 21.25%..   21.25% is closest to 22% in the choices..   ans 22%
<result>E</result>
By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 meters, inclusive, the breadth is between 1 to 1.1 meters, inclusive and the height is between 2 to 2.1 centimeters, inclusive. If the actual length, breadth and height of the box do indeed fall within the respective ranges estimated by the carpenter, which of the following is the closest to the maximum possible magnitude of the percentage error W that the carpenter can make in calculating the volume of the rectangular box?