The measurements obtained for the interior dimensions of a rectangular box are 200 centimeters by 200 centimeters by 300 centimeters. if each of the three measurements has an error of at most 1 centimeter, which of the following is closest to the 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 correct option is C) 160,000 cm³

Step-by-step explanation:

Consider the provided information.

It is given that for each of the three measurements has an error of at most 1 centimeter.

Consider the length and width of the rectangle is 200 and height is 300.

Let change the length by 1 cm. Then the change in volume is:

1×200×300 = 60,000 cm³

Let change the width by 1 cm. Then the change in volume is:

200×1×300 = 60,000 cm³

Let change the height by 1 cm. Then the change in volume is:

200×200×1 = 40,000 cm³

Now add them to get the maximum possible difference:

60,000+60,000+40,000=160,000 cm³

Hence, the correct option is C) 160,000 cm³