A rectangular block with a volume of 250 cm³ was sliced into two cubes of equal volume. How much greater (in sq. cm) is the combined surface area of the two cubes then the original surface area of the rectangular block?

### Concept & Slicing Solids When a solid is sliced into two pieces, the total volume remains identical, but the combined surface area increases because new faces are created at the slice. Specifically, slicing a block into two exposes two new faces. $$ \text{Increase in Area} = 2 \times \text{Area of the Cross-Section} $$ ### Step-by-Step Solution * The total volume of the rectangular block is $250\text{ cm}^3$. * It is sliced into two identical cubes. Therefore, the volume of one cube = $\frac{250}{2} = 125\text{ cm}^3$. * Find the side length of the cube: $a^3 = 125 \Rightarrow a = 5\text{ cm}$. * The slicing creates two new faces, one on each of the newly formed cubes. * These new faces are squares with side length $a = 5\text{ cm}$. * Area of one new face = $5 \times 5 = 25\text{ cm}^2$. * Since the slice separates the block into two, it exposes two such faces. * Increase in total surface area = $2 \times 25\text{ cm}^2 = 50\text{ cm}^2$. ### Exam Strategy & Shortcut Recognize that slicing any shape into two adds exactly two cross-sectional faces to the total surface area. Since the halves are $125\text{ cm}^3$ cubes, their faces are $5 \times 5 = 25$. Two new faces mean $2 \times 25 = 50$ extra surface area. No need to calculate total areas! ### Common Pitfall Wasting time calculating the total surface area of the original block and the total surface area of the two cubes, then subtracting them. While this works, it is prone to arithmetic errors and takes much longer. ### Final Answer Therefore, the correct answer is **50**.