Question

The dimensions of a rectangle box are consecutive integers. If the box has volume of 13,800 cubic centimeters, what are its dimensions?

Answer 1

If the dimensions were all the same number ... the box was a cube ...
then each dimension would be  (the cube root of 13,800) cm.

         ∛13,800 = 23.986... (rounded)

so the place to look is around 23 .

(22 x 23 x 24)  =  12,144     <==  too small; go up one integer

(23 x 24 x 25)  =  13,800     <==  Eureka !    

The consecutive integers are  23,  24,  and  25 .