A cube of edge length 6 cm is sliced into 20 congruent pieces by vertical cuts perpendicular to a base of the cube and parallel to a face. The total surface area of the 20 pieces exceeds the surface area of the original cube by x square centimeters. What is x? (Do NOT include punctuation in your answer.)

 Oct 21, 2020

The original surface area is still there obviously....but each new slice (twenty of them )  increases the surface area by the area of two faces

   EXCEPT for the two end faces which only increase the area by ONE face (as the other face was part of the original surface area)

       so originally  each face was 6x6 = 36  cm2          (and the surface area was 6 x 6 x 6  = 216 cm2 )

               now add  18 slices with two faces    18 x 2 x 6 x 6    and two slices with one face  2 x 6 x 6

                   for a total increase of   1368 cm2

 Oct 21, 2020

16 Online Users