Answer:
The total surface area of the 20 pieces exceeds the surface area of the original cube by 1368 square centimeters.
Step-by-step explanation:
The formula of surface area for the entire cube ([tex]A_{s,c}[/tex]), measured in square centimeters, is:
[tex]A_{s,c} = 6\cdot l^{2}[/tex] (Eq. 1)
Where [tex]l[/tex] is the side length, measured in centimeters.
If this cube is sliced into 20 pieces, the surface area of each slice ([tex]A_{s,s}[/tex]), measured in square centimeters, is equal to:
[tex]A_{s,s} = 4\cdot \left(\frac{1}{20}\right)\cdot l^{2}+2\cdot l^{2}[/tex]
[tex]A_{s,s} = \frac{1}{5}\cdot l^{2}+2\cdot l^{2}[/tex]
[tex]A_{s,s} = \frac{11}{5}\cdot l^{2}[/tex] (Eq. 2)
And the surface area of all slices ([tex]A_{s,as}[/tex]), measured in square centimeters, is:
[tex]A_{s,as} = 44\cdot l^{2}[/tex] (Eq. 3)
Then, we calculate the excess of surface area ([tex]\Delta A[/tex]), measured in square centimeters, by applying the following formula:
[tex]\Delta A = A_{s,as}-A_{s,c}[/tex]
[tex]\Delta A = 44\cdot l^{2}-6\cdot l^{2}[/tex]
[tex]\Delta A = 38\cdot l^{2}[/tex] (Eq. 4)
If [tex]l = 6\,cm[/tex], then the excess of surface area is:
[tex]\Delta A = 38\cdot (6\,cm)^{2}[/tex]
[tex]\Delta A = 1368\,cm^{2}[/tex]
The total surface area of the 20 pieces exceeds the surface area of the original cube by 1368 square centimeters.
