Discussion
A solid cube of side 12 cm is cut into small solid cubes of side 4 cm each. What will be the relation between the total surface area of the original cube and the new total surface area of the small cubes so formed ?
Answer: A
The new total surface area will be thrice the original.
The big cube makes \((12/4)^3 = 27\) small cubes.
\[ \begin{aligned} \text{original} &= 6 \times 12^2 = 864 \text{ cm}^2 \\ \text{new} &= 27 \times 6 \times 4^2 = 2592 \text{ cm}^2 \\ 2592 \div 864 &= 3 \end{aligned} \]
Cutting creates new faces, so the total area increases, not decreases. In general, cutting into cubes of 1/n the side multiplies the surface area by n, here 3.
The volume stays the same, 1728 cm3, because no material is lost; only the exposed surface grows.
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