A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area? 

200%

If side of larger cube = 3x

then to cut 27 identical cubes, side of smaller cube = x

Total surface area = 6 (side)²

Now,

            Large   :    One Small Cube

Side :      3       :         1

T.S.A:     6(3)²  :      6(1)²

                9      :       1

            Large   :    27 Small Cubes

T.S.A. :     9       :   (1 × 27) 

                9      :       27

                1      :       3

Total surface area increase by  = 3 - 1 = 2

Increase percentage = \(\frac{2}{1}\) × 100 = 200%