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.)

Guest Oct 21, 2020

#1**+1 **

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 cm^{2 }(and the surface area was 6 x 6 x 6 = 216 cm^{2 })

^{ }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 cm^{2}

ElectricPavlov Oct 21, 2020