A cuboid of size 100 cm $$\times$$ 80 cm $$\times$$ 60 cm cut into eight identical parts by three cuts. What is the total surface area (in square cm.) of all the eight parts?

When a cuboid is cut into eight identical parts by three cuts, then the length, breadth, and height of the each new cuboid will be half of the earlier. There will be eight new cuboids.

Length of each new cuboid = L = $$\frac{100}{2}$$ = 50 cm

Breadth of each new cuboid = B = $$\frac{80}{2}$$ = 40 cm

Height of each new cuboid = H = $$\frac{60}{2}$$ = 30 cm

Total surface area of all the eight parts = $$8\times\ \left[2\left(LB+BH+LH\right)\right]$$

= $$8\times\ \left[2\left(50\times40+40\times30+50\times\ 30\right)\right]$$

= $$8\times\ \left[2\left(2000+1200+1500\right)\right]$$

= $$8\times\ \left[2\times\ 4700\right]$$

= $$8\times9400$$

= $$75200\ cm^2$$