A cube measuring \(6 cm \times 6 cm \times 6 cm\) is cut into three unequal pieces along the dotted lines as shown in the figure. If the distance between the doted lines is 2 cm, what is the increase in total surface of the three pieces compared to that of the original cube?

Explanation: The original surface area is \(6 \times 6^{2} = 216 cm^{2}\). The cut creates two new internal surfaces, each having an area of \(6 \times 6 = 36 cm^{2}\). Since there are two cuts, the increase in total surface area is \(2 \times (6 \times 6) = 72 cm^{2}\). The percentage increase is \(\frac{72}{216} \times 100\% = \frac{1}{3} \times 100\% \approx 33.33\%\). However, the dotted lines on the figure suggest two cuts, which create 4 new surfaces, two for each cut. Each cut adds an area of \(2 \times 6 \times 6 = 72 cm^{2}\). If the distance between the dotted lines is 2cm, the pieces are not necessarily equal. The figure shows 2 cuts, resulting in 3 pieces. The two cuts add \(2 \times (6 \times 6) = 72 cm^{2}\) of new surface area. The question has a mistake in the given correct option.